The article dismisses most of the objections previously forwarded in this journal by Khandakar Qudrat-I Elahi against Amartya Sen's framework for famine analysis: the entitlement approach. Instead, the article argues that even thirty years after the conception of the entitlement approach, it remains a potent framework for famine analysis, as illustrated by the recent 2005 famine. However, as contemporary famines are increasingly linked to factors that have hitherto received limited attention in entitlement analysis -conflicts, legal collapses and political struggles -the article calls for supplementary famine analysis on the meso and macro levels.

The Entitlement Approach  a case for framework development rather than demolition

Introduction

In 1977, Sen forwarded a simple yet groundbreaking idea: what if we think of famine as a lack of access to food rather than a lack of food availability? This basic insight was developed into a more comprehensive famine framework, the entitlement approach, in Amartya Sen's famous book Poverty and Famines: An Essay on Entitlements and Deprivation from 1981. Its publication sparked much controversy and heated academic debate about the validity of the entitlement approach and the empirical evidence supporting the framework.

Some thirty years later, two things are painstakingly evident: the approach has yet to fully catch on in the famine prevention policy work of donor countries, international organisations and national governments alike; and the critique of the approach remains very much ongoing. Of course, debate and reflexivity is the very foundation of a dynamic social science tradition. Nevertheless, the discussion surrounding the entitlement approach has not always been productive, as it was largely based on misconceptions and straw men fallacies. Ravallion summed up the debate about Sen's entitlement approach by proclaiming that 'in retrospect, I do not think one could reasonably say that all of this debate has been insightful or interesting' [START_REF] Ravallion | Famine and Economics[END_REF](Ravallion :1209)). Jean Drèze argued -referring to the quality of some of the contributionsthat the entitlement debate is likely to be of greater interest to psychologists than economists (Drèze 1999:5). (JDS 2006:541-557).

The idea of revitalising the discussion of the entitlement approach is indeed commendable in as much as it is currently both underutilised and seems ripe for a brush-up in terms of being applied to more contemporary famines -a point I will further elaborate on in the course of this article. However, the quality of the published article is such that it does not distinguish itself sufficiently from many of the earlier critiques to constitute a constructive platform for augmentation or further development of the famine analysis discipline. Part of the reason is that the article is conspicuously silent when it comes to the question of how to move forth. And part of the reason is Elahi's obsession with analysing the entitlement through an ethical lens as a philosophical approach. Therefore, while I sympathise with Elahi's effort to inject fresh ideas and critiques into the entitlement debate, having devoted some time myself to the analysis of famine in general and Sen's entitlement approach in particular, I feel obliged to address some of the shortcomings and misunderstandings presented in the article.

Firstly, allow me to familiarise the reader with the essence of Sen's entitlement approach.

Presentation of Sen's entitlement approach

Sen's entitlement approach broke with the traditional view of famine analysis referred to by Sen as the Food Availability Decline approach (henceforth the FAD approach).

The FAD approach was a response to the Malthusian focus on population growth as a problem in itself. Being conceived in an era (mid-nineteen century) when significant agricultural advances were made, the FAD approach contained an optimism not reflected in the Malthusian tradition: mankind was not the passive victim of nature's own checks and balances. Instead, the approach was concerned with means of ensuring sufficient food availability. According to the FAD approach, the cause of famine was that food production was concentrated geographically or in time. Some countries (or regions) did not have enough food during particular periods of time to prevent famines. Natural disasters, inadequate production techniques or lack of infrastructure could all contribute to the lack of food. Accordingly, the approach focused on food production capacities. Sen's critique of the FAD approach did not signal a return to the Malthusian tradition.

On the contrary, Sen distanced himself from both approaches by constructing an approach in which famines were neither reduced to nature's own checks and balances nor the result of an insufficient production capacity; instead, famines were to be analysed in a socio-economic context. His approach was thus a refutation of the well known Malthusian pessimism as well as a dismissal of what Sen described as 'Malthusian optimism': as long as there is enough overall food in the economy, there is no reason to worry (Sen 1993:36).

Sen defines the entitlement of a person as 'the set of alternative commodity bundles that can be acquired through the use of the various legal channels of acquirement open to that person' (Drèze/Sen 1989:23;Drèze/Sen 1990a:38). A person's entitlement depends on two factors: his initial endowment and the E-mapping specifying the set of alternative commodity bundles that can be obtained given the initial endowments. The E-mapping will often depend on the exchange entitlement that describes the alternative commodities that can be obtained in exchange for the endowments, but it can also be influenced by changes in production or direct transfers. An adverse change in the Emapping can therefore be caused by an endowment loss, failure of production, exchange failure and transfer failure. Entitlement failure occurs when it is not possible for a person to acquire commodity bundles with enough food to survive (Sen 1981:51).

By including the E-mapping in the entitlement approach, Sen attempted to improve the understanding of poverty and famine by taking a more disaggregated perspective. He thereby acknowledges the massive economic activity usually taking place in impoverished households at a disaggregate level. The change in income transfers among the poor themselves is of paramount importance in famine situations. Hence, a famine does not occur because of lack of food availability but from a wide variety of unfavourable changes in the E-mapping and endowment variables such as rising food prices, falling wages, falling cash crop prices and so forth. Access to food is not merely reduced to an economic question but 'depends on the legal, political, economic and social characteristics of the society in question and the person's position in it' (Sen 1981:46). Sen does not deny that food availability affects many of the factors included in the E-mapping -it does -merely that the central problem is the change of entitlement (Sen 1977:34). Through a lovely double negation, Michael Watts (2000:60) notes that ' Sen (1981:162) refers to as a 'general approach for analysing famines rather than one particular hypothesis about their causation.' In his critique of the entitlement approach, Devereux (2002:1) also notes that the entitlement concept is descriptive rather than normative and that entitlements derive from human legal rights rather than moral or human rights.

Commenting on Elahi's critique of the entitlement approach

In an article entitled Entitlement failure and Deprivation: a Critique of Sen's Famine Philosophy, Elahi forwards a critique against the conceptual foundation of the entitlement approach in the form of four specific objections that are emphasised in his abstract: a) Sen unduly criticises the FAD approach. The FAD is indeed fully capable of explaining movements in food prices.

b) Sen's exchange entitlement is inconsistent with the principles of capitalism, since this economic system operates on the conceptual and legal approach of voluntary exchange.

c) In as much as food is considered an entitlement commodity, other basic necessities of life, such as healthcare and education, could then claim the same status.

d) Finally, it is argued that the approach is founded on a hidden hypothesis that income distributions in non-communist states are economically and politically optimal. Despite the preoccupation of many distinguished scholars with the entitlement approach and several academic debates over the past thirty years, the four listed objections have not previously been uncovered, Elahi's argument goes, because the previous critique has all appeared 'too uncritical to pinpoint the logical lacuna in Sen's famine thesis' (Elahi 2006:542). I will address each of these objections in turn, but allow me briefly to return to the title of Elahi's article. In the preceding thirty years, Sen's entitlement approach has been perceived to be a specific hypothesis or a theory of famine causation, but not even the harshest critics of the entitlement approach have ever claimed that Sen had developed a famine philosophy. A Google search reveals that the term famine philosophy is anything but a conventional term -it has only been used by Elahi himself. I would argue that Sen's approach to famine analysis does not constitute a philosophical direction, as it has little to do with belief systems and ethical principles. Instead, the entitlement approach is an analytical approach, making it possible to deduce conclusions with moral implications; one of those implications, for instance, relates to the inadequacy of relying on legal structures in famine situations.

The title therefore already appears to merit some reservations with respect to the validity of the criticism that is about to be forwarded in the main text.

To claim that the approach is philosophical in that 'it connects the critical ideas of all four aspects of our social life -economic, legal, political and social' (Elahi 2006:556) does not appear to be a valid argument. The mere connecting of different strands does not constitute a philosophical direction -in effect, most analytical approaches strive towards being able to encompass various socio-economic aspects. The fact that Elahi has -fallaciously as I will expand in the following -converted an analytical approach into a famine philosophy might account for some of the misconceptions in his article.

Note that I fully sympathise with many of the moral issues Elahi raises in his article; it is not hard to applaud his concern for questions of inequality, poverty and famine. Yet contrary to Elahi's belief that socio-economic issues of poverty and famine 'must be studied from the perspectives of moral and political philosophy' (Elahi 2006:556), I would argue that it is imperative that these issues are studied using a coherent analytical approach and that such analysis enhances rather than hinders subsequent moral and ethical judgements. Elahi's second objection against the entitlement approach is based on the rather bombastic claim that 'Sen's idea of entitlement contradicts the fundamental principle of market economy' (Elahi 2006:552). Elahi argues that the term exchange entitlement is inconsistent with the principles of capitalism and that the whole entitlement approach is 'tantamount to the repudiation of capitalism and advocacy for the revival of socialism' (Elahi 2006:553). The reason is that the market is based on voluntary exchanges and that Sen's idea of food entitlement is inconsistent with these voluntary exchanges. I strongly disagree with this contention. Every capitalist society builds on institutional arrangements that are not merely based upon voluntary principles of economic exchange. They provide their citizens with certain entitlements (often in the form of a minimum of pension, education, healthcare, unemployment benefits and so forth) and expect certain obligations (income tax, VAT, military service and so forth). The state itself is the most extreme institutional arrangement that serves the dual purpose of forming and controlling the environment for voluntary exchange but at the same time often intervenes in the market to improve market institutions or to pursue political goals (equity, poverty reduction and so forth).

In addition, Sen's use of the term exchange entitlement does not contain any ethical considerations of legal rights to food (as one might find in a famine philosophy); instead, Sen clearly defines exchange entitlements in purely analytical terms as the set of alternative bundles of commodities that a person can acquire in exchange for what he owns (Sen 1981:3). Sen directly asserts that the measurement of poverty should not be an ethical exercise but primarily a descriptive one (Sen 1981:23). As such, entitlements do not contradict voluntary exchange; the concept simply does not contain any normative notion of food entitlement at the expense of voluntary exchange.

Furthermore, Elahi perceives it to be a contradiction that Sen's 'famine philosophy' accepts that endowments created by the market are legitimate, while at the same time holding the system responsible for failing to meet the food entitlement of poor people (Elahi 2006:553). However, Sen's position is exactly that endowments are not legitimate in a Nozickian sense; instead, he holds that starvation deaths reflect legality with a vengeance. This has been pointed out repeatedly not just by Sen but other scholars as well; as recently as 1997 Ravallion -looking back at some of the critiques against the entitlement approach -specified exactly this point: 'The term "entitlement" has also generated some confusion. The term carries a normative connotation, although the intended meaning in this context is entirely positive; Sen (1981, p. 2) was careful to point this out, and specifically to distinguish his usage of the word from the normative meaning found in, for example, Robert Nozick's (1974) "entitlement theory of justice"' [START_REF] Ravallion | Famine and Economics[END_REF](Ravallion :1210)). Endowments created by the market might be legitimate in a legal sense, but by analysing famines through the entitlement approach, one can conclude that widespread suffering and deaths can take place in an otherwise fair legal approach. Legitimacy then becomes a moral question that lies beyond the analytical approach.

On Elahi's third objection

The third objection against the entitlement approach is caused by the same misconception as above. Elahi rightly -and hardly surprisingly -argues that the poor might not be able to afford sophisticated healthcare services in some societies, but he then argues that 'according to Sen's theory, they are not entitled to have this service, because it is not included in their endowment set' (Elahi 2006:554). Again, this confuses Sen's analytical approach with ethical reflections of whether the poor ought to enjoy access (and to what extent) to education, employment, healthcare, housing etc.

Notwithstanding the fact that the entitlement approach is an approach for famine analysis (and not for poverty alleviation or public policy targeting in a broader sense), the entitlement approach is indeed able to analyse whether individuals do in fact have access to sophisticated healthcare exactly because the E-mapping includes an array of different channels including government healthcare provisions. What policy conclusions to draw from such an analysis is an open question. And on that note, it is worth remarking that sophisticated healthcare services are in fact restricted to relatively few in most societies -even in wealthier societies.

On Elahi's fourth objection

As regards the last point, Elahi argues that 'the entitlement approach is founded on a hidden hypothesis that income distribution in the non-communist state is economically and politically optimal. This hypothesis, too implicit to attract readers' attention must be controversial beyond any shadow of doubt' (Elahi 2006:556). Elahi might have a point here. Indeed, the hypothesis must be very implicit, because I have not seen any arguments in Sen's work that could be even remotely interpreted in that manner. Why the entitlement approach should presume an income distribution that is economically and political optimal (optimal in what way?) remains a mystery that Elahi fails to get across. In addition, such an optimal income distribution in non-communist states resonates rather poorly with Elahi's previous claim about the entitlement approach being a repudiation of capitalism and advocacy for the revival of socialism.

On Elahi's other claims

Aside from the four objections above that were emphasised by Elahi himself in the abstract and his conclusion, his article also contains other debatable claims that must be addressed briefly.

Elahi contends that economic and legal systems can be described objectively and descriptively, while social and political systems cannot be encompassed in a descriptive approach on the grounds that they are unavoidably prescriptive and normative (Elahi 2006:553). Following this logic, Sen's entitlement approach cannot merely be an analytical approach, as it also seeks to include social and political factors.

A distinction between social and political systems on one side and economic and legal systems on the other is bound to be artificial: social and political factors create/shape/destroy economic and legal systems and vice versa. Upholding distinctions can be merited from an analytical perspective but not as an ontological position, which contends that social and political systems are prescriptive, while economic and legal systems are descriptive. To postulate that social and political factors cannot be analysed descriptively goes against the basic fundamental principles driving much of the research in political science, sociology and anthropology.

Entitlements derived from state contributions (mainly political) and from family reciprocity (mainly social) can certainly be analysed just as well as entitlements derived from the market (mainly economical).

In another section, Elahi blames the E-mapping for including social security provisions, because 'these social security provision are available, to a varying degrees, only in advanced democratic countries of the West, which naturally questions whether the entitlement approach applies to famines that occur, or had occurred, in third world countries' (Elahi 2006:550). This line of reasoning is flawed on at least two levels: (i) including a rarely used channel in a variable hardly invalidates the whole approach.

The entitlement approach with its E-mapping can obviously also be applied in cases developing countries due to their limited logistical capacity for implementing a progressive taxation system based on direct taxes [START_REF] Burgess | Taxation and Development[END_REF]. Social security systems in developing countries rely less on voluntary insurance systems with an emphasis on capability expansion and more on state provisions prioritising the protection of vulnerable groups from external shocks. In famine situations, these provisions might be inadequate, belated, suffer from problems of leakage and corruption, or they might be used politically in a counterproductive manner, but claiming that they are available only in developed countries is simply incorrect. In famine situations, aid from international NGOs -often channelled directly through the government -further enhances the role of public provisions.

In the article, it is also asserted that 'the entitlement approach contributes to the process of landlessness and pauperization' (Elahi 2006:554). Aside from seemingly exaggerating the political impact of the entitlement approach, the statement builds on the -rather unfounded -inference that public policy based on the entitlement approach would force subsistence peasants to liquidate their assets in order for them to receive public assistance. Such serious accusation must be founded on a minimum of empirical evidence. Public policy could certainly be construed in a manner providing perverse incentives, but there is nothing in the entitlement approach that could be responsible for spurring such a type of public policy.

Elahi also argues that 'the situation of starvations eliminates all kinds of choices' (Elahi 2006:556), which ought to invalidate the entitlement approach, because it builds on neoclassical theory with individual choice as the guiding principle. Aside from noting the ambiguity of having an approach that on one side builds on neoclassical economic theory and at the same time supposedly should contradict the fundamental principles of market economy, Elahi is once more on troublesome ground when he claims that starvation eliminates all kinds of choices, as the many choices faced by starving people have both been empirically observed and can be explained theoretically. Ravallion

Developing the entitlement approach

Let me hasten to admit that there is indeed scope for analytical improvements of the entitlement approach. The crux of the matter is that this does not even remotely lead me to concur with Elahi's conclusion (2006:556) that 'Sen's innovative idea has added little to a penetrating analysis, let alone a solution to this disgraceful human tragedy.'

On the contrary, I find Sen's entitlement approach to be an extremely potent approach to famine analysis, and I regret when it falls short of being fully utilised in the general policy work on famine. The 2005 Niger famine provides a case in point for the continued relevance of the approach as well as being illustrative of the lack of adherence to the approach's basic principles in much practical famine policy work. ii The famine, it seems, was caused less by a food availability decline and more by an increase in the price of staple foods.

According to the USAIDs Famine Early Warning System Network (FEWS NET), the national cereal production was only 11 percent down from the five year average -and could have been covered by a mere 3% increase in Niger's normal cereal imports (IRINnews 2005/08/09). The production was even above the relatively poor 2000/1 season, which did not lead to a major food crisis (Gobler-Tanner 2006:1). Moreover, the same crop failure was experienced throughout the Sahel region, but no other country faced a food crisis of famine proportions (HPG 2005:1). Much of the reason for the 2005 famine was Niger's rigid economic structures that pressured people to sell grain to traders when prices were at their lowest and to borrow grain from them when prices were at their highest. These unfavourable terms of trade led to exchange entitlement collapses for many households in the Southern districts. The problem in Niger was not an absence of food -there was indeed food in the market -people could simply not afford to buy it (Mousseau & Mittal 2006:11).

The famine was allowed to develop because both the government and much of the international community seemed to rely on aggregate measures of food production.

The FEWS early warning system -with an emphasis on drought and weather-related factors rather than socio-economic factors -failed to anticipate the severity of the famine. As late as December 2004, FEWS NET described the overall regional food situation in Sahel as fair in terms of availability and access with only localised problems (HPG 2005:3). The exponential increases in feeding center admissions across the Southern regions of Niger (as documented by Médecins Sans Frontières) were not caught in an early warning system based mostly on vegetation and rainfall indicators.

Thus, the 2005 Niger famine underlines the continued need to more thoroughly incorporate the focus of the entitlement approach regarding socio-economic access to food in early warning systems.

My argument is rather that many contemporary famines (the Niger famine being one of the exceptions) involve slightly different dynamics that make it necessary to rely on additional analytical tools to strengthen the entitlement analysis. I will focus on three such dynamics here. Firstly, there needs to be increased focus on the ties between conflict and famine.

Empirically, contemporary famines appear to be strongly correlated with the existence of civil war. The reason is not only that conflict generates more famines now compared to thirty years ago, but rather, that fewer contemporary famines take place outside the realm of conflict and war. FAO (2005:5) reports how conflict has moved up to become the most common cause of food insecurity. Another recent FAO report (Kidane et al. 2006:22) estimates that food access was constrained in 2001 by political or armed conflicts in more than half the countries in Sub-Saharan Africa, most commonly because warring parties used food directly as a weapon or otherwise destroyed local food supplies and capacities to produce food.

Secondly, an entitlement analysis needs to address the collapse of legal structures.

The formal legal system has limited applicability in many famine-prone countries, and the importance of socially enforced rules might be greater than Sen had envisaged in It should be emphasised that my point is not that famines were previously isolated from the effect of politics, war and the breakdown of formal legal structures. iii It is rather that famines have become more directly linked to civil war, the absence or downright Allow me to elaborate further on how to expand the entitlement analysis to better address these three characteristics of modern famines

The entitlement approach and conflict Despite the recent surge in conflict-related famines, scholars claimed long ago that Amartya Sen downplayed the role of war. Nolan (1993:21) notes that 'the areas worst affected by famine in both the 1970s and the early 1980s were those also worst affected by warfare.' And yet, Nolan agues, wars are grossly overlooked in Amartya Sen's famine analyses. Kula's (1987) main argument in his article is that the real reason for most famines is 'war and its complicated politics, which affect the supply system as well as creating a decline in entitlements' (Kula 1987:112). These views have been summarised under the heading, a 'military famine thesis' by [START_REF] Jenkins | Food Security in Less Developed Countries 1970 to 1990[END_REF].

The strong connection between conflict and famine appears to indicate that Nolan & Kula were correct in claiming that Sen downplays the role of conflict and war. The words 'conflict and 'war' do not even figure in the subject index in Poverty and Famines. Although, the impact of wars can be caught in the entitlement approach (war often leads to an immediate collapse of entitlements), it might be argued that such a powerful event calls for a more direct inclusion in an analysis than the indirect influence through the entitlement-variable. According to von Braun et al. (1998:3), of the 21 identified famines in the period 1970-1998, 15 were at least partly triggered by war.

Note, however, that this says little of the strength of the link between war and famineit merely indicates that when a famine occurs, war is likely to be at least partially to in arms imports as percentage of GDP enters highly significantly with the expected negative sign in all regressions. However, child undernutrition was found not to depend on that variable, but rather on a proxy for genocide/politicide that displayed equally strong attributes (highly significant with the expected negative sign).

This could indicate that military build-up (and possibly war) affects food production but not as such vulnerability to hunger; however, in genocidal environments (where legality is undermined and state aggressions are targeted at particular ethnic or political groups), the effect on hunger vulnerability is felt directly. [START_REF] Howard-Hassmann | Genocide and State Induced Famine: Global Ethics and Western Responsitbity for Mass Atrocities in Africa[END_REF] points to the connivance of famines as a weapon of war: if a government starves its people to death rather than actually murdering them, it can pretend to the outside world that the deaths were accidental rather than deliberate. A newer strand of famine literature thus examines the rationale and feasibility of encompassing famine crimes in international law [START_REF] Marcus | Famine Crimes in International Law[END_REF]).

In the case of war, the collapse of legal structures appears to cause the greatest suffering. Kula (1987), [START_REF] Waal | War and Famine in Africa[END_REF] and von Braun et al. (1998:20-25) describe some of the numerous ways that war can contribute to famine: through transfers of food to the army, inflationary pressure from the war, through the shortage of labour caused by enrolment to the army and war casualties, and through infrastructural breakdown. By far the greatest contributor to modern famines, however, is the looting and raiding of impoverished villages, often in connection with civil wars. This 'systematic asset-stripping' -as de Waal (1993:38) articulates it -has been a major contributor to famines on the African continent: in the former Zaire, Sudan, Rwanda and Somalia. War by itself is not a sufficient condition for famine. Indeed, even though -according to Kula (1987:113) -the British forces during World War II had the best food available and the rest of the population was put on a very basic diet, Sen reports that in that period, the British life expectancy rate at birth actually rose substantially compared to other decades (Drèze/Sen 1989:180). This anecdotal finding further supports Jenkins & Scanlans' (2001) result that military build-up and war affects the overall supply of calories but does not seem to have an impact on hunger. In the war/famine relationship, legal/institutional collapse together with some political interest in upholding the famine must be included as the most important factors. Sen was therefore correct in arguing that the famines included in his book occurred in societies with legal structures intact, but perhaps he failed to consider or anticipate how most recent famines have coexisted with some type of violation of legality during war.

This, however, brings the discussion to the entitlement approach's reliance on legal structures, which will be discussed in the subsequent section.

The entitlement approach and legal structures

In the context of modern famines, one of the key challenges is to capture the collapse of formal and informal legal structures in the entitlement approach. In the approach's original conception, entitlements were based on acquirements through formal legal structures. These legal structures might not even be present in some developing countries; or to the extent they are present, they could still be very poorly defined, arbitrary and likely to be violated in extreme situations such as war and famine. If the country is characterised by deep social cleavages or even in a civil war, this will be even more so. The problem with relying on legal structures was not unfamiliar to Sen, as he acknowledged that there can be a good deal of vagueness on property rights and related matter in pre-capitalist societies, which would cause 'fuzzy' entitlements (Sen 1981:48-49).

The legal limitation could be argued to be a logical consequence of his approach -and to a certain extent a useful one. [START_REF] Gore | Entitlement Relations and 'unruly' Social Practices: A Comment on the Work of Amartya Sen[END_REF] and [START_REF] Gasper | Entitlement Analysis: Relating Concepts and Contexts[END_REF][START_REF] Gasper | Sen's Capability Approach and Nussbaum's capabilities ethic[END_REF] describe how the approach -at least in part -was developed as a response to Nozick's principles of moral entitlement, which built on the sanctity of individual's possessions and the protection of property rights regardless of consequences. According to their interpretation, Sen's approach is not only a critique of the previous FAD approach but also a moral critique of Nozick's possessive individualism. The fact that ILO financed

Poverty and Famines makes their interpretation even more plausible; ILO would of course be very interested in counteracting Nozick's liberalistic views. Sen treats legal structures as an independent variable and shows that within such structures, destitution and famine can take place. Sen ends Poverty and Famines with exactly that point: 'Starvation deaths can reflect legality with a vengeance' (Sen 1981:166). Yet, although the formal legal system is indeed an important institution in converting available food to food entitlements -it is not the only institution. could also result from a shift in the practice of law, the customary laws, or be a product of socially enforced rules. The formal legal systems in many African countries have failed to integrate the customary laws, and the formal systems remain inaccessible for the majority of the population. [START_REF] Kane | Reassessing Customary Law Systems as a Vehicle for Providing Equitable Access to Justice for the Poor[END_REF] describes how the informal customary law is more important for many people in developing countries as opposed to the legal structures of civil law, which are limited to the relatively few. Customary law is usually defined as a type of established pattern of behaviour within a particular social setting that is perceived to be law by the relevant actors and that therefore lead to certain legal practices that can be objectively observed. Access to resources in African countries is often determined less by individual property rights and more by ownership relations based on ethnicity or seniority for groups, communities and tribes rather than individuals. Gore (1993:449) provides an empirical example of food scarcity in Ghana (in the 1970s) that not only affected the E-mapping through higher prices but also through the existing moral rules in the society where being a regular customer determined whether or not it was possible to buy at given prices. A somewhat similar argument is presented by [START_REF] Woldemeskel | Famine and the Two Faces of Entitlement: A Comment on Sen[END_REF] with reference to the Ethiopian famines in the 1970s. At that time, having nominal legal access to land did not enable you to cultivate it. The agricultural relations were constructed in such a manner that the state was provided with the real or possessory right to land (Woldemeskel 1990:493). As such, the peasants might have had de facto access to endowments, but they lacked the institutional licenses to transform the endowment into food. The mapping was determined by the practice of law rather than by the nominal legal rights. Both of these examples point to the insufficiency of relying solely on formal legal channels of acquirement.

In 1989, Sen introduced the term extended entitlement, which he defined as 'the concept of entitlements extended to include the results of more informal types of rights sanctioned by accepted norms of legitimacy' (Dreze/Sen 1989:11). There is no doubt that informal rules and social norms play a decisive role in understanding famine but Sen's own application of the term is quite similar to a two-stage analysis (inspired by economic analysis), whereby he first determines the household's entitlement set and then the allocation of food within the household (Drèze/Sen 1989:79). The original entitlement term is used in the first part of the analysis, while the 'extended entitlement' is used in the second part. Sen has thereby really only included part of the informal institutions in the analysis; for instance, the role of religiously induced informal rules at a more aggregated structural level is overlooked. Such a static two-stage analysis also leaves the dynamics of the interplay between different types of rules unanalysed. Sen has therefore rightfully been accused of not accepting the full consequences of explicitly introducing social conventions and norms in the entitlement mapping (Leach et al. 1999:233). Gore (1993:429) even argues that Sen 'ignores how legal rules work in practice and downplays the way in which socially enforced moral rules constrain and enable entitlement.' Barbara Harriss-White's (1990:351-424) analysis of gender relations in situations of hunger and famine, for instance, benefits from a broader analytical perspective that is capable of incorporating impacts of patriarchal discrimination despite the article's strong quantitative base. Michael Watts, while being very supportive of the approach in general, also argues (2000:61) that the E-mapping should be 'much more complex and dynamic (involving all manner of social, cultural, institutional, and collective actions beyond the entitlements discussed by Sen).' Osmani (1991:591 ) acknowledges that 'the question of legality creates problems for the entitlement approach' but argues further that if the entitlement set was not based on acquirement through legal structures, the set would be indeterminable because one could always -by means of violence -extend his/her set of entitlements. These structures do not need to take the form of formal legal institutions, and in a later article Osmani (1995:254 [START_REF] Sage | Breaking Legal Inequality Traps: New Approaches to Building Justice Systems for the Poor in Developing Countries[END_REF] argue that discussions of legal rules too often ignore the fact that they are social constructions -cultural and normative understandings establishing and legitimising appropriate behaviour. Instead of starting from a 'rule of law' model from which deviations can be measured and targeted, it may be more helpful -and realistic -to 'assume anarchy'. Legal anarchy with the collapse of both formal and informal legal structures appears to be an integral cause of many contemporary famines.

Seeing that legal systems continuously adapt to the dominant moral rules in society and that these rules could quickly change in the context of civil wars or disasters, famine analysis needs to recognize the legal system more as a dynamic process than a static structure.

The legal foundation of the entitlement approach creates opportunities as well as drawbacks. In modern famines, the drawbacks appear to be greater than Sen had envisaged in 1981. [START_REF] Devereux | Sen's Entitlement Approach: Critiques and Countercritiques[END_REF] seems to be correct in noting that confining the analysis to legally enforceable property rights is a restrictive way of viewing famine.

The legal point of departure appears to facilitate an economically based analysis while impeding a broader political analysis. The formal legal system has limited applicability in many famine-prone countries, and most contemporary famine situations seem to coexist with legal collapse. This legal anarchy during famine highlights the need not only to include informal social structures and cultural practices in the approach (that is a necessary requirement) but also to analyse legal systems endogenously to gain an understanding how they operate under stress.

The entitlement approach and the political level

Operating at the micro-level alone, the entitlement approach needs additional analytical tools to improve its capacity at the political level. Several writings explicitly or implicitly point out the need to include a political perspective in the approach to famine (De Waal 1997, [START_REF] Keen | The Benefits of Famine[END_REF][START_REF] Crow | Understanding Famine and Hunger[END_REF]). Keen states that Sen's approach fails to account for 'the possibility that states and politically powerful groups may actively promote famine and actively obstruct relief for rational purposes of their own' (Keen 1994:5). Watts (2000:62) emphasises that entitlements are not externally given but constituted and reproduced through conflict, negotiation and struggle. Famines -as other socioeconomic phenomena -always serve different interests and are therefore inherently related to struggles of power. Famines can be directly manipulated and in some cases even purposely created to obtain a given policy objective.

In Exploiting food as an instrument for political objectives is not just limited to a few authoritarian military states in the developing world. The CIA regarded the US food surplus in the 1970s as a very important factor of dominance, and the command over food could be used to destabilise fragile regimes (Shephard 1993:88). According to [START_REF] Shephard | Some Tragic Errors[END_REF], this strategy was used during the 1981-1985 Ethiopian famine. For two years, the US deliberately obstructed and delayed US food aid to the Mengistu government that was under strong communist influence at the time.

It is imperative to recognise that most famines do indeed contain strong political elements. Although famines can be triggered by economic shocks or natural disasters, modern famines are inherently political -increasingly intertwined in political agendas and power struggles. If the entitlement failure is caused by deliberate political action rather than unintended market/government failures, the approach would have limited explanatory power if not supplemented with analysis at the political level. Following the internal logic of the approach, famines are always per definition explained by entitlement failures, but the approach's liberal assumptions and micro-level perspective makes it an ill-suited approach within which to understand the deliberate use of famine as part of a political or military strategy. Nor does it provide any strong clues about how to analyse these political dynamics. The many different interests involved in controlling and manipulating a famine are simply not integrated into the approach. This does not make the approach redundant in famine analysis; the entitlement approach is an excellent analytical approach at the micro-level. However, if some famines are deliberately constructed as part of a political agenda, then the approach would benefit from supplementary political analysis on the macro or meso levels. The entitlement approach can capture important proximate causes of famine that could be used to devise effective policy responses; yet more fundamental forces of famine will often reside at the macro-level, and supplementary analysis is called for to grasp the political dynamics so vital in modern famines. iv

Conclusion

Sen's basic expectation to his approach is not difficult to replicate, as he makes it quite explicit: 'The entitlement approach provides a general approach for analysing famines rather than one particular hypothesis about their causation' (Sen 1981:162). Elahi, however, erroneously seems to assess the approach as a famine philosophy -and he does so without empirical evidence to back most of his objections and without carving out alternatives for famine analysis. This article found that his main objections to the entitlement approach did not stand up to closer scrutiny and that the entitlement approach still remains a very beneficial approach for famine analysis exemplified by the 2005 Niger famine. The entitlement approach merely needs adjusting to the new dynamics of contemporary famines. Sen himself argued (1981:45) that his entitlement approach 'makes no attempt to include all possible influences that can in principle cause starvation for example illegal transfers (e.g. looting), and choice failures e.g.

owing to inflexible food habits.' Sen simply argued that the limitations were in most cases not of a magnitude that would justify a shift away from the micro-level foundation based on legal entitlements. Nevertheless, it is clear that the reliance on legal structures and a benevolent government is possibly a greater limitation than Sen imagined -particularly in times of civil war and conflict. Contemporary famine is widespread, precisely in contexts characterised by ethnic strife, weak market integration, fuzzy property rights and group-based customary law. As human-induced famines have increased substantially in recent decades, so too has the need to further develop and strengthen the entitlement approach with analyses on the macro and meso levels.

Tools to move forward

So while access to food should continue to be the founding principle in famine analysis, many contemporary famines would benefit from an analytical focus on the macro and meso levels as well. Several practical tools that can strengthen the entitlement analysis with increased information regarding political and institutional famine dynamics on the meso and macro levels are readily available. Allow me to end this article by briefly pointing out a few.

In order to capture the influence of informal legal structures on famine vulnerability, one could turn to the Sustainable Livelihoods Approach that builds on the idea that vulnerable people draw on a range of material and non-material assets to pursue multiple strategies in the face of an external shock. v This approach was conceived in its present form in the late 1990s by DFID. Concretely, the approach often maps individual or group assets according to an asset pentagon comprising the five key groups of natural, physical, human, financial and social capital assets (shaped by informal legal structures and cultural practices). According to this approach, people's ability to strategically draw on these assets in the face of a famine will determine their survival potential and long-term livelihood. Thus, although this type of approach shares the micro-level foundation of the entitlement approach, the broader scope encompasses informal structures and cultural practices and -as an additional advantage -it has already been widely applied by development agencies and international NGOs (DFID, FAO, UNDP, WFP, CARE to name a few), which warrants some institutional expertise in its application. An FAO study of food insecurity in Nepal based on this type of approach revealed that although certain groups officially had equal access to schools, drinking water, health centers and other community facilities, in practice their access was less than equal due to social exclusion based mainly on caste.

To obtain an overview of the more aggregate institutional and political aspects of famine, simple qualitative tools such as Stakeholder Analysis, Institutional Analysis and Political Mapping can be applied. The aim of a stakeholder analysis would be to identify key stakeholder characteristics, their interests, and the nature and degree of their influence on famine formation and famine prevention. Political mapping can be used to illustrate (spatially) the relationship between the key stakeholders in the political landscape of famine policy. The purpose could be to identify different existing fractions within and between the government, the media, donor countries and international NGOs with respect to famine interventions. Institutional Analysis can be used to examine the rules that govern the identification of famine and the negotiation over the implementation of policy reforms. Institutions can both be formal (legal system and property rights on which the entitlement approach is mainly based) and informal i PRSPs describe the country's macroeconomic, structural and social policies and programs over a three year or longer horizon to promote broad-based growth and reduce poverty, as well as associated external financing needs and major sources of financing.

ii Many major international organizations have restrained from categorizing the Niger food crisis as a famine. However, with reported mortality rates peaking around 1.7/10.000/day and an excess mortality in the thousands, it seems reasonable to argue that the food crisis indeed took on famine proportions.

iii With some of the most apocalyptic famines in the century, the 1932-1933 Soviet famine and the 1958-1961Chinese famine, being "manmade" such a conception would be absurd. iv The author wishes to thank JDS referee 1 for drawing my attention to the useful distinction between proximate and fundamental causes of famines. Elahi quotes Sen as saying 'that people must not be allowed to become so poor that they offend or are hurtful to society. It is not so much the misery and plight of the poor but the discomfort and cost to the community which is crucial to this view of poverty. We have a problem of poverty to the extent that low income creates problems for those who are not poor.' This is a blatant misquotation, as these are actually the words of Martin Rein (1971) -not Amartya Sen. Elahi then asserts that 'Sen's moral posture about the poor' can be summed up in the following paragraph from Poverty and Famine (1981:9): 'To live in poverty may be sad, but to "offend or [be] hurtful to society", creating "problems for those who are not poor" is, it would appear the real tragedy.' This is a gross misrepresentation of Sen's moral position generated by conveniently leaving out to the very next line, where Sen states 'It isn't easy to push much further the reduction of human beings into "means".' Sen's standpoint is precisely that 'the focus of the concept of poverty has to be on the well-being of the poor', and that the views expressed above are 'grotesque' and should be 'dropped without further ado' (Sen 1981:9-10). Thus, Sen's stance on poverty and deprivation is the exact opposite of the questionable moral concern for the non-poor, which There is no need to speculate as to Elahi's motives for wanting to undermine Sen's credibility and morality, but there is every need to condemn such a smear campaign based on misquotations and misrepresentations in an academic debate.

F

Admittedly, it is difficult to have a fruitful academic debate if the scholarly combatants do not share the basic premises for the debate. And although Elahi's clarification that by 'philosophy' he does in fact mean 'science' in general is a welcome step forward, many unresolved issues still remain. Elahi believes that he does not need to include any empirical evidence to substantiate his numerous claims. Empirical evidence is irrelevant, for instance, when Elahi claims superiority of the FAD approach over the entitlement approach; and it is irrelevant when claiming that FAD is fully capable of explaining food prices in all food situations. I would disagree. Furthermore, Elahi does not apparently believe Ad 2) Although I am pleased to see that the entitlement approach now merely changes the nature of a market economy instead of being inconsistent with the principles of capitalism, as per Elahi's original claim, I still lack a valid reason for why the entitlement approach -or rather, policies based on the approachwould fundamentally change the nature of a market economy when the myriad of far more wide-ranging policies do not.

Ad 3) The entitlement approach is not inherently long-or short-term. The collapse of endowments (due to drought or illness) is often short-term, and there is nothing methodologically preventing this from being analyzed in the entitlement approach. Moreover, the fact that an analytical framework has been developed to analyze famine and food security issues can never logically in any way 'disqualify the poor from entitlement of many life-saving services' such as education and healthcare.

2

  Living up to the agenda of opening up many new areas of debate about vital development issues, the Journal of Development Studies published a critique of the entitlement approach by Khandakar Qudrat-I Elahi in May 2006

  are non-existent exactly because the E-mapping includes a diverse range of other channels. (ii) Government provisions in developing countries are in fact widespread in most famine situations in the form of food distribution, fair price shops or public works. Every single Poverty Reduction Strategy Paper I have come across includes policies for social security provisions. i It could even be argued that the public policy expenditure side plays a much more important redistributive role in

  has approached famines from an economically founded risk and uncertainty assessment where choosing to starve could be a step in a rational long-term survival strategy.[START_REF] Devereux | Sen's Entitlement Approach: Critiques and Countercritiques[END_REF] has conversely emphasised what he refers to as 'social vulnerability', where social units (often families) are forced to make choices about whom to sacrifice in order for the unit to survive. Despite differences in perspectives, both contributions highlight the aspect of choice during famine.Elahi claims that starvation by connotation is associated with an involuntary endurance of hunger, and he uses this to criticise Sen for being unclear and missing this main point, because Sen has argued that starvation can both be caused by a person being unable to command enough food or caused by a person not using his ability to avoid the situation(Elahi 2006:549). Nonetheless, the connotation applied by Elahi is neither shared by the Encyclopaedias of Medicine nor the dictionaries of Merriam Webster and Oxford (nor any other I have come across), where there is no reference whatsoever to the aspect of involuntariness with respect to starvation. In addition, one might wonder how Elahi would describe the craving sensation felt by the famished mother who voluntary surrenders her own food to feed her severely malnourished children; or the sensation felt by the subsistence farmer who chooses to starve now rather than to harvest early and jeopardise the household's existence in the long run.The final point I will address here isElahi's postulation (2006:555-556) that Sen's 'entire analysis is founded on posterior food supply situation.' In as much as Sen has spent 300 pages explaining the perils of focusing on food supply, I would think this claim requires no further repudiation.

  1981. With up to 90% of the population in parts of Sub-Saharan Africa relying on customary legal relations, attention to informal structures seems particularly warranted(Woolcock & Sage 2005:20). In addition, most contemporary famines seem to coexist with rapidly changing or collapsing formal and informal legal arrangements, which calls for the inclusion of these legal arrangements as dynamic practices rather than as static, exogenous structures.Finally, increased attention should be devoted to understanding famine dynamics at the political level. The entitlement approach, with its liberal assumptions and micro-level perspective, is somewhat ill-equipped to understand the deliberate use of famine as part of a political strategy. WithFAO (2005:6) noting that the proportion of food emergencies that can be considered man-made has increased over time from 15 percent in the period 1986-91 to more than 35 percent between 1992 and 2003, understanding dynamics at the political level has become an increasingly indispensable component of famine analysis.

  structures, and political manipulation. Today, there are few famines that do not involve these features, and the socio-economic context surrounding the famines presented in Sen's Poverty and Famine book is somewhat uncharacteristic of contemporary famines. In none of the empirical examples that Sen used to show the superiority of the entitlement approach -the 1943 Bengal famine, the 1974 Bangladeshi famine, the 1972-1974 Ethiopian famine and the 1971-74 Sahel faminesdid these three factors stand out. If Sen were to choose four famines today, the chances of him picking four famines in which these features do not dominate would be nil.

  Legal, nominal access to entitlements might not be sufficient to prevent entitlement failure due to other socioeconomical structures that might hamper such access. Entitlement failures and famine

  Zimbabwe in 1983Zimbabwe in -1984, a famine was intentionally created in Matabeleland by means of blockades intended to strangle an uprising by the anti-government ZAPU movement(De Wail 1997:59).Alexander (1991) describes how the government's fifth brigade not only murdered thousands of civilians, but also pursued a policy of withholding food from local areas where the ZAPU movement enjoyed support. The same atrocities took place in Somalia 1991-1992, where the southern Somalis had a history of political marginalisation. This escalated to looting and confiscation during the leading to widespread migration and famine. In the 1983-1985 Sudan famine, the Sudanese People's Liberation Army even openly acknowledged the obstruction of food as a weapon of war(Keen 1993:16). More recently in Zimbabwe, Mugabe again pursued famine-triggering policies, albeit less directly than in the beginning of the 1980s. In 2003, Mugabe encouraged veterans of the 1965-1980 war of independence to invade white-owned farms. While previously enjoying status as the breadbasket of Africa, half of Zimbabwe's population was considered food insecure by 2003 (and Zimbabwe was now known as 'the land of the empty plate'). The policies not only drove food production down, but the situation was used to serve political purposes: most of the veterans were Mugabe supporters; Mugabe distributed food to political supporters and withheld it from his political opponents; and he refused to permit international food agencies into the country to help the starving(Howard-Hassmann 2005:502).

  Elahi attempts to affix to Sen. The Nobel Prize Committee (1998) explicitly acknowledged Sen's devotion 'to the welfare of the poorest people in society', , another Nobel Laureate, characterized Sen as 'the conscience of economics' (quoted in India Today Magazine 1998).

  in contributing with suggestions as to how the research agenda should move forward. Again I would beg to differ. If Sen's entitlement approach is truly useless (or even counterproductive), what then is Elahi's recommended direction for contemporary famine analysis? Instead of presenting the readers with a Wikipedia-like reproduction of David Hume's Treatise of Human Nature that remains strangely detached from the rest of his reply, despite Elahi's grandiose claim of wanting to examine my critique 'in the light of Hume's philosophy of human knowledge', I would rather have had him elaborate on these important matters.There is really no need to deal with Elahi's rebuttal in great depth, as I believe my objections still stand strong. I have no qualms leaving it to the reader to decide whose observations and objections are 'logically weak' and 'deficient from an . Allow me, however, to end with the following brief remarks:Ad 1) Elahi incorrectly claims that Sen ignores the fact that speculative -not actual demand -determines food prices, not because Sen is a Nobel Laureate in Economics, but because Sen is indeed attentive to speculative demand; a point for which I have provided concrete evidence.

Ad 4 )

 4 As Elahi appears capable of uncovering hidden hypotheses in Sen's writings that have eluded both Sen himself as well as all other scholars for 25 years, it is indeed a waste of academic resources not to have Elahi more engaged in empirically based research and in moving the famine research agenda forward. In the absence of Elahi's endeavors in this regard, one must settle for my article above specifying the implications of contemporary famine characteristics; or -for a more comprehensive study -one could turn to The New Famines, edited by StephenDevereux (2007), which forcefully articulates a change in the thinking about famine, i.e. viewing famines as political outcomes rather than failures of food availability or access to food.

  explicitly recognizes the need to take a broader view on legality 'to mean conforming to established social norms and practices, and not merely to what is sanctioned formally by the state.' Still, this view treats legal structures as exogenous variables with less consideration to how the structures institutionalise themselves, how they are transformed, and the conditions under which they disintegrate. Woolcock &

  Even in the Niger famine, where the entitlement approach seems to fit perfectly, there is much additional information to be gathered from the most cursory interest in the political level. Niger's President Mamadou Tandja denied that Niger was experiencing famine because, as he told some BBC reporters, 'the people of Niger look well-fed' (BBC News August 12, 2005); he then proceeded to speak of 'foreign propaganda' and 'deception' by aid agencies in their attempt to raise funds and maintained that the 'situation has been exaggerated for political and economic gain by opposition parties and the UN agencies (quoted in The Independent 2005). Although the entitlement approach could help explain the disaggregated impact of the famine, it is not difficult to see how a famine could evolve under such political leadership.

	(cultural practices and social norms that are more peripheral to the approach). Again,
	the institutional analysis can be conducted as a mapping exercise depicting the
	resources and responsibilities of agencies and organisations involved with
	implementing policies relevant for famine protection.
	The previous description of how Zimbabwe's Mugabe exploited food for political ends
	to reward supporters and withhold food from political opponents was easily uncovered
	F o r using such basic techniques. F o r F o r F o r
	P P P P
	e e e e
	e r e r e r e r
	R R R R
	e e e e
	v i e v i e v i e v i e
	w w w w
	O n l O n l O n l O n l
	y y y y
	23

The Entitlement Approach -A case for framework development rather than demolition'

  An excellent and more in-depth analysis of the applicability of the Sustainable Livelihoods Approach in the field of famine research can be found in Joseph A. Yaro's article Theorizing food insecurity: building a livelihood vulnerability framework for researching food insecurity in the Norwegian Journal of GeographyVol. 58, 2004.

	Rejoinder: 'Elahi's 2006 article subjected Amartya Sen's entitlement approach to numerous
	criticisms: the approach contradicted the fundamental principle of market
	economy; it was based on a hidden hypothesis that income distributions in non-
	communist states are economically and politically optimal; and it contributed to a F process of landlessness and pauperization. Unfortunately, Elahi continues down o r the same path of unsubstantiated accusations in his response to my article, 'The Entitlement Approach -a case for framework development rather than o r e R e v i e l n y l O n O w w e i v e R r e e r e P P demolition'.
	y
	1
	27

v

URL: http://mc.manuscriptcentral.com/fjds Journal of Development Studies


A Cozza

F Canavero

B Démoulin

A Closed-Form Formulation for the Total Power Radiated by a Single-Wire Overhead Line

A new analytical solution for the total power radiated by a single-wire line over a ground-plane is here proposed, for the special case of a lossless complex exponential current-distribution. The line is not assumed to be electrically short or "closed", thus being suitable for assessing the emission/immunity of actual transmissionlines as in the automotive domain. A practical procedure employing this model is proposed and it is shown to excellently agree with the experimental results obtained in a mode-stirred reverberation chamber. An application to unshielded multi-conductor transmission lines (MTL) is also proposed.

I. INTRODUCTION

The transmission-lines used as interconnects between two or more electronic devices act more and more as antennas, thus providing the main "access" for radiated interferences. In particular, in the automotive domain MTLs are usually unshielded, so that they play a major role in EMC emission/immunity tests. These are usually performed by measuring the intensity of the electromagnetic field at a certain distance for several orientations of the equipment under test (EUT), thus characterizing it by a sort of near-field radiation pattern. This sort of tests are usually performed in semi/fully anechoic chambers, thus simulating an ideal open area/free-space test site. Although providing reproducible results, this procedure is quite time-consuming, requiring a number of measurements for characterizing the EUT. Recently, several authors have suggested another kind of test, i.e. measuring the total radiated power (TRP) [START_REF] Wilson | Emission and Immunity Standards: Replacing Field-at-a-Distance Measurementes with Total-Radiated-Power Measurements[END_REF], [START_REF] Hill | Radiated Emissions and Immunity of Microstrip Transmission Lines: Theory and Reverberation Chamber Measurements[END_REF]. The TRP has been historically measured by several means [START_REF] Krogerus | Evaluation of Three Methods for Measuring Total Radiated Power of Handset Antennas[END_REF], all of them requiring the complete characterization of the EUT's radiation pattern which, for electrically large devices, strongly depends on the EUT geometry and excitation. A simpler and far more effective way of providing an estimation makes use of mode-stirred reverberation chambers (MSRC): a statistical evaluation of the TRP is thus provided and can be related to the maximum radiated field by considerations on the EUT electrical dimensions [START_REF] Wilson | On Determining the Maximum Emissions From Electrically large Sources[END_REF].

Although this procedure is profitable for testing an EUT, the numerical computation of the TRP still requires a great deal of time, because of the double-integration of the power density over an EUT-bounding surface. Although many analytical results are available in antenna theory for electrically short linear current-distributions (CD), only one attempt has been made (to our knowledge) for an electrically long line [START_REF] Storer | Radiation resistance of a two-wire line[END_REF]: anyway the line was assumed to be electrically very close to the ground-plane. On the other hand, in recent years several groups have pursued new models for extending the classical TLT to a wider frequency range, in order to include higher modes, especially radiation ones [START_REF] Nitsch | Telegrapher equations for arbitrary frequencies and modes: Radiation of an infinite, lossless transmission line[END_REF][7] [START_REF] Maffucci | Full-Wave Transmission-Line Theory[END_REF]. Although these techniques provide a very powerful tool for high-frequency modelling of transmission-lines, their actual implementation is far from accessible to the average industrial user.

The aim of this paper is to present an analytical solution for the TRP of an overhead single-wire line, with no geometry-based approximation (e.g. an electrically short line), for the special case of a lossless complex exponential current-distribution. This case, although not valid for very "open" lines, is still valid for a wide frequencyrange, allowing for a simple and effective assessment of radiation losses, and thus of the line emission/immunity features.

II. THE MODEL

The system here considered is a uniform single-wire line of finite length L , hanging above a boundless metallic ground-plane (Fig. 1). The analytical formulation is based upon the following hypothesis:

1) the thin-wire approximation holds for the overhead conductor 2) the ground-plane is lossless and boundless 3) the medium surrounding the line is lossless 4) the current-distribution along the line can be described as the sum of two complex exponentials, as in [START_REF] Hill | Radiated Emissions and Immunity of Microstrip Transmission Lines: Theory and Reverberation Chamber Measurements[END_REF], implying that the line is lossless 5) the radiation due to the discontinuities introduced by the line ends is supposed to be negligible, i.e. the line is regarded as the main source of radiation or as the main "access" for coupling to radiated interferences. Even though hypothesis 4) may seem pointless, the radiation losses will be taken into account afterwards by using a two-step procedure (see section IV).

The loads and the voltage generator in Fig. 1 are just regarded as mathematical boundary conditions rather than physical connections; the actual effects of vertical risers will be discussed in section IV.

The TRP is defined by equation [START_REF] Wilson | Emission and Immunity Standards: Replacing Field-at-a-Distance Measurementes with Total-Radiated-Power Measurements[END_REF], where Ω is a closed bounding-surface embracing the entire system, S is Poynting's vector and n is the unitary outward vector normal to surface Ω. Due to the hypothesis of an ideal ground-plane, this surface can be reduced to a hemisphere laying on the ground-plane (0 < ϑ < π, -π/2 < ϕ < π/2), being the e.m. field identically equal to zero on and beneath the metallic bound. For the very same reason, the image principle can be invoked, so that the actual system can be substituted by an equivalent two-wire line in free-space. Furthermore, being the medium lossless, every integration surface is equivalent, yielding the same amount of TRP. Hence, an hemisphere whose radius goes to infinity can be chosen, exploiting the simpler farfield expressions for the radiated magnetic field H(ϑ, ϕ), yielding:

P r = Re Ω S • ndΩ = Ω ζ 0 |H(ϑ, ϕ)| 2 dΩ (1)
being ζ 0 the characteristic impedance of the surrounding medium. Variables ϑ and ϕ refer to figure 1: the former is the angle between the direction ρ and the axis z, the latter is the azimuthal angle considered on the xy plane. The following lossless modal description for the CD has been used:

I(z) = I + 0 (e -γz -Γ L e -2γL e +γz ) (2)
where I + 0 is the forward-travelling modal current, γ = γ 0 ξ is the purely imaginary propagation constant for the wave guided by the line and Γ L represents the load reflection coefficient. The parameter γ 0 = jk 0 is the propagation constant of the surrounding medium, so that ξ acts as a sort of equivalent permittivity for the propagation along the line. The resulting expression for equation ( 1) is:

P r = |I + 0 | 2 ζ 0 4π 2 π 0 +π/2 -π/2 sin 3 ϑ |ξ 2 -cos 2 ϑ| 2 • • sin 2 (k 0 h sin ϑ cos ϕ)|B(ϑ)| 2 dϕdϑ (3) B(ϑ) = (e -γ0(cos ϑ+ξ)L -1)(cos ϑ -ξ) + (4) -Γ L e -2γL (e -γ0(cos ϑ-ξ)L -1)(cos ϑ + ξ)
After some quite long algebraic manipulations, equation (4) can be rewritten as:

|B(ϑ)| 2 2 = (ξ 2 + 1)σ + (ξ 2 -1)τ κ c + sin 2 ϑ[τ κ c -σ] + -cos(k 0 L cos ϑ)[(ξ 2 + 1)σκ c + (ξ 2 -1)τ ] + sin 2 ϑ cos(k 0 L cos ϑ)[σκ c -τ ] + -2σξκ s cos ϑ sin(k 0 L cos ϑ) (5)
where σ = 1 + |Γ L | 2 , τ = 2Re {Γ L e -γL }, κ c = cos(k 0 ξL ) and κ s = sin(k 0 ξL ). In order to solve equation (3), the double-integral has to be factorized into two one-dimensional integrals. An easy and straightforward solution employs McLaurin's expansion of sin 2 x, which eventually yields expression (6)

P r = |I + 0 | 2 ζ 0 4π 2 ∞ n=1 a n π 0 sin 2n+3 ϑ |ξ 2 -cos 2 ϑ| 2 |B(ϑ)| 2 dϑ (6) a n = - k 0 h n 2 a n-1 (7)
being a 0 = -π/2. The terms present in integral (6) share the same structure which, though being analytically solvable, has no simple closed-form solution. Nevertheless, the special cases ξ = 1 and ξ 2 -cos 2 ϑ ∼ = ξ 2 provide a closed-form result [START_REF] Gradshteyn | Table of Integrals, Series, and Products[END_REF], which is exact for ξ = 1:

P r ∼ = |I + 0 | 2 ζ 0 ξ 4 π 2 ∞ n=K+1 a n-K S 2n+1 (τ κ c -σ) + + S 2n-1 [(ξ 2 + 1)σ + (ξ 2 -1)τ κ c ] + -ψ n [(ξ 2 + 1)σκ c + (ξ 2 -1)τ ] + + ψ n+1 σκ c -τ -2σξ k o L 2n κ s (8)
S n = π/2 0 sin n ϑdϑ = S n-2 n -1 n (9)
ψ n = J n-1/2 (k 0 L ) (k 0 L /2) n-1/2 √ π 2 (n -1)! (10)
being K = 0 for ξ = 1 and K = 2 otherwise. This result can be dramatically simplified by neglecting Bessel's terms ψ n ; in fact, they play a relatively minor role, as shown in the results presented in Fig. 2a.

III. NUMERICAL VALIDATION

In order to check the validity of expression (8) as a solution for equation [START_REF] Wilson | Emission and Immunity Standards: Replacing Field-at-a-Distance Measurementes with Total-Radiated-Power Measurements[END_REF], it has been compared with the numerical integration of (1), performed by using an algorithm based on Lobatto's adaptive quadrature. In particular, this check is important for verifying whether the series expansion is fast-convergent or not, as well as for assessing the solution performance when approximating a line with ξ > 1. To this end, a single-wire line with h = 10 cm, L = 1 m, V s = 1 V and Z s = Z L = 50 Ω has been considered, over a frequency range attaining 1 GHz. This means that around 1 GHz the line would be some three wavelengths long, i.e. an electrically long line.

The first check, involving the series convergence, considered the case ξ = 1. The results are shown in figure 2a, where the TRP obtained through numerical integration is compared with approximated solutions considering just one term and three terms with the further simplification discarding the terms related to Bessel's functions. Figure 2 proves the good convergence properties of the proposed solution, together with the fact that even the first expansion term provides a good estimation of the TRP. The fact that Bessel's function can be neglected comes from their argument k 0 L , which makes functions ψ n negligible for an electrically long line. Fig. 2. The results from the convergence test for ξ = 1 (a) and the comparisons between the numerical integration of (1) (dashed lines) and equation ( 8) (solid lines).

The other check was related with the approximated solution for ξ > 1. In this case equation ( 8) provides a very good result even for ξ = 1.4 (figure 2b), which does not fully satisfy the condition ξ 2 -cos 2 ϑ ∼ = ξ 2 . On the other hand, whenever ξ ∼ = 1, it is possible to use equation [START_REF] Maffucci | Full-Wave Transmission-Line Theory[END_REF] for the case ξ = 1, but for an actual value not equal to one. An example is shown in figure 2b, where for ξ = 1.05 the expansion for ξ = 1 has been employed: the maximum error is smaller than 3 dB. The ability of the solution to extend its agreement with the exact solution for ξ > 1, even in case of just a few percentage points, will be shown to be very useful for applying it to actual lines (see section V).

Another important point in favour of an analytical approach to TRP, even when flawed by strong assumptions and approximations , is the fact that the numerical evaluation of (1) is far less simple than it may appear. In fact, since we are considering an electrically long line, the radiation pattern is not "well behaved" as for an electrically short linear antenna. Indeed, it is characterized by a great number of side lobs, and thus a great number of zeros. The integration of such a function has to be carried out with due care, since even small interpolation errors around these zeros can lead to overall errors about some decibels.

IV. APPLICATION TO A SINGLE-WIRE LINE:

EXPERIMENTAL VALIDATION Equation ( 8) is not just a formal solution to the TRP for a lossless exponential current distribution, but it can be effectively used for assessing the TRP for an actual single-wire line. To prove that, a mock-up line as the one in figure 1 has been prepared. In this case, the line was kept hanging through two vertical risers (VRs), whereas the line's ends were connected to two N-type connectors underneath the ground-plane through two via-holes. The first connector was used for loading the line with N-type calibration loads, and the other one was connected to a coaxial cable for the line excitation. The immediate consequence of using this mock-up is the breaking of assumptions no. 2) and 5), i.e. the ground-plane has now a limited surface and VRs are bound to be an important radiation sources.

In order to measure the TRP for this system, an MSRC has been used. Although these facilities are usually employed for generating a statistically uniform and isotropic e.m. field, in this case we used it as a means for measuring the power radiated by the system along several directions without moving the receiving antenna. Indeed, adopting for the sake of simplicity a ray description, the fact that the MSRC's walls are metallic leads to multiple reflections, therefore the e.m. energy received by an antenna placed into the MSRC will include contributions from a great deal of radiation directions coming from the mock-up. Furthermore, the MSRC are equipped with a stirrer, whose task is to change the boundary conditions inside the MSRC, therefore modifying the reflection pattern and allowing the receiving antenna to measure the contributions to the radiated power as from a different set of directions. Hence, measuring the received power for a large number of stirrer's positions and computing the average received power involves an estimation of the power radiated all over an infinitely large sphere, the same as performing the flux integral expressed in [START_REF] Wilson | Emission and Immunity Standards: Replacing Field-at-a-Distance Measurementes with Total-Radiated-Power Measurements[END_REF]. The experimental setup is sketched in figure 3. The stirrer was set to perform a complete turn in 7 s, by 360 finite steps for each frequency investigated. Since the MSRC's dimensions were 1.9x2.65x2.9 m, the minimum frequency for which the chamber can be regarded as overmoded is about 700 MHz. The line was fed by a function generator kept outside the MSRC and connected to the line through a coaxial cable passing through a via in the MSRC's wall.

In the same way a horn (SWR = 2.2 over 0.7÷3 GHz) was used as the receiving antenna, connected to a spectrum analyzer outside the MSRC. The entire procedure was run by a software controlling all the devices through a GPIB interface. The result of this procedure is not yet a correct evaluation of the TRP: in fact, the MSRC insertion loss has to be assessed. The insertion loss includes cable losses, mismatches and the MSRC's own insertion loss (its Q is not infinite). Because of this, the line has been substituted by another horn antenna (identical to the receiving one), and the entire procedure has been repeated. By subtracting the resulting received power (expressed as dBm) from the first evaluation of the TRP, a good evaluation of the actual TRP is obtained.

Before applying equation ( 8), we need to assess the importance of VRs. To this end, the entire mock-up line, including the VRs, was simulated using NEC2 (method of moments) comparing it with the results obtained by the proposed two-step procedure (afterwards in this section) which neglect the VRs's radiation. An example of these results is shown in figure 4, for h = 3 cm and L = 80 cm and the line's far-end short-circuited. As expected, due to the differential configuration of the horizontal line, its radiation efficiency is very poor at low frequencies, where the two vertical monopoles dominate the TRP. Anyway, as the electrical length of the horizontal line increases, its radiation grows stronger and the VRs can be neglected. On the other hand, as he frequency increases, the attenuation along the line gets more important, reducing the contribution coming from the horizontal line, thus leaving only the near-end VR to radiated. Although the VRs's radiation has been neglected, their effects on the propagation have been considered as proposed in [START_REF] Degauque | Remarks on the transmission-line approach to determining the current induced on above-ground cables[END_REF]. Indeed, their being taken into account is very important to correctly identify the resonances position. In order to use equation ( 8) with an actual line, it has be applied cunningly. Another of the basic assumptions which is no more valid is no. 4), i.e. the line can not be considered as lossless. Indeed, the very idea of a TRP means that part of the power propagating along the line is radiated away. It has been proved in [START_REF] Daniele | Spectral theory of a semi-infinite transmission line over a ground plane[END_REF] that the propagation along a line over an ideal ground-plane can be acceptably described by a single TEM mode as long as the ratio h/λ 1/3. Thus, the CD can be described as the sum of two exponentials, but a more general approach requires the introduction of an exponential attenuation, as in figure 5, whereas equation ( 8) requires the CD to be uniform. Nevertheless we are not interested in the actual CD, but rather in the effect of the CD for the sake of TRP. So we could consider an equivalent CD, with no loss over a certain length, exactly in the same way as for the current excited by an e.m. field penetrating into a conductive medium; indeed, we can regard this current as uniformly distributed on an equivalent portion known as skin-effect penetration depth. The same idea has been applied in figure 5 this approach is that the attenuation constant has to be assessed. Being related to the radiated field, the radiation losses are dependent on the entire CD. This means that it does not suffice just to know the line's cross-section as for the p.u.l. parameters: therefore they cannot be generally treated as ohmic losses. Furthermore, the presence of discontinuities such as VRs could introduce privileged sources of radiation, thus making pointless the definition of a p.u.l. radiation resistance. Indeed, that would mean to spread all over the entire line an effect that is perhaps concentrated in a limited region, such as for a VR.

Anyway, for the special case of an infinitely long uniform line, the radiation losses act as ohmic losses [START_REF] Nitsch | Complex-Valued Transmission-Line Parameters and Their Relation to the Radiation Resistance[END_REF], therefore a p.u.l. radiation resistance can be defined and included in the p.u.l. impedance, thus accounting for the radiation losses. The same procedure can be pursued for a finite-length line [START_REF] Wendt | Radiation losses representation in the transmission-line theory[END_REF], as long as the VRs's contribution is negligible (we are neglecting all type of fringing effects): in this case the line finiteness is taken into account by the CD itself, which includes a backward-travelling wave. Hence, what is needed is to compute the radiation resistance R r . This can be accomplished by using the following definition:

R r = P r |I + 0 | 2 1 (1 + |Γ L |) 2 (11)
referring to the CD introduced in (2), i.e. with no losses. In fact, even though this CD does not necessary suit the actual CD, it provides an acceptable estimation of R r . Now it is possible to compute the attenuation constant as:

α = Im (z e + R r /L )y e (12)
where z e and y e are respectively the p.u.l. impedance and admittance for the TEM mode (or quasi-TEM considering ohmic losses). Equation ( 8) can be used by considering the modal parameters I ± 0 computed with the new CD including radiation losses, but for a reduced length L eq = 1/α (obviously L acting an an upper-bound), as in figure 5. Moreover, the resulting P r is weighed down by a factor w 2 :

w = 1 -e -αLeq αL eq (13)
accounting for the attenuation along the equivalent length L eq , thus considering the equivalent weighed CD as in figure 5. Some experimental results are shown in figure 6: the line under test was short-circuited at the far-end with h = 3 cm, L = 80 cm; the wire's diameter was 1.5 mm and the ground-plane dimensions were 60 cm and 120 cm. The TRP was studied in the frequencyrange 700 MHz ÷ 3 GHz, hence considering the line as electrically long. The agreement between the proposed model and the experimental result is quite good, with an average absolute error about 2 dB. Figure 6 also points out the importance of assessing the radiation resistance before computing the actual TRP.

0.5 1
The procedure here described, although apparently lengthy, is actually very simple and straightforward, being basically made up by two steps, i.e. the evaluation of the line radiation resistance and the actual TRP, through the definition of an equivalent CD. Because of this simplicity and straightforwardness, we think that this procedure is suitable for industrial purposes, as a compromise between a theoretically sound description and a far more approximated solution. Its main limitation is its being based on a quasi-TEM propagation model; hence, it is valid as long as the ratio h/λ holds [START_REF] Daniele | Spectral theory of a semi-infinite transmission line over a ground plane[END_REF]. V. AN APPLICATION TO MTLS Since a single-wire line is not very common in industrial applications, we had to focus our attention on MTLs. Although equation ( 8) holds just for a single-wire line, it can be usefully employed for an MTL above a metallic ground-plane. Actually, in EMC the most dramatic effects regarding the radiated emission/immunity problems are due to the common-mode (CM) current, or bulk current I b (z). Let us consider the modal description for the CD along a N -wire MTL:

I(z) = T P + (z)I + m0 -P -(z)I - m0 (14)
I b (z) = N i=1 I i (z) = N i=1 T i I m (z) = QI m (z) = N i=1 N k=1 T ik I m,k (z) (15)
where T is a square matrix relating the modal currents to the physical ones, P ± (z) = diag(exp(∓γz)) are the propagation matrices, γ is the vector of the line's propagation constants and I ± m0 are the excitation factors for the forward-and backward-travelling modal-currents. The e.m. field radiated by an MTL is mainly due to the CM current, as long as the line's conductors are "packed" together, being the cross-section position of the i-th wire identified as y = d i and x = h i . This assumption requires

k 0 | h -h i | 1 and k 0 | d -d i | 1 ∀i ∈ [1, N ],
where h and d stand for the averages on h i and d i . Let us consider an overhead uniform MTL: the magnetic field can be expressed, in the far-field, as:

H(ϑ, ϕ) = φ γ 0 4πρ sin ϑe -γ0ρ N i=1 e -γ0hi x•ρ e -γ0di ŷ•ρ • • Γ N k=1 T ik I m,k (z)e -γ0zẑ•ρ dΓ (16) ∼ = φ γ 0 4πρ sin ϑe -γ0ρ e -γ0hx•ρ e -γ0dŷ•ρ • • Γ I b (z)e -γ0zẑ•ρ dΓ (17)
The integration-path Γ describes the entire CD and its image. The right-hand approximation holds for a "packed" line using (15), and shows that the main contribution to the radiated field is due to the CM current. The importance of this result lays in the fact that whenever the CM current can be approximated as the CD along a singlewire line, equation ( 8) can be usefully employed for estimating the TRP for an MTL. Indeed, this usually holds in several cases of actual interest, e.g. for unshielded MTLs employed in the automotive domain. For these cases the single-wire CD of the CM can be derived from the modal description:

I b (z) = I + b0 e -γ b z -I - b0 e +γ b z (18)
I ± b0 = I ± m0,j N i=1 T i,j (19)
where γ b corresponds to the CM's propagation constant in γ, as its j-th element. Furthermore, for a line as the one in Fig. 7, the CM is always identified as the one with the smallest propagation constant. This is due to the fact that the electric field force-lines are mostly in air rather than in the wires' coating, whereas the differential modes present the opposite situation. On the other hand, for a homogeneous medium γ i = γ ∀i ∈ [1, N ], so that the previous procedure is no more available. In this case P ± (z) = exp(∓γz)I so that:

I b (z) = Q[I + m0 e -γz -I - m0 e +γz ] = I + b0 e -γz -I - b0 e +γz (
20) This procedure has been applied to the line shown in Fig. 7, characterized by a dielectric coating with r = 3, computing matrices T and γ by a moment method [START_REF] Clements | Computation of the Capacitance Matrix for Systems of Dielectric-Coated Cylindrical Conductors[END_REF]. The analytical solution is compared with the numerical computation of the TRP, by inserting equation ( 16) into [START_REF] Wilson | Emission and Immunity Standards: Replacing Field-at-a-Distance Measurementes with Total-Radiated-Power Measurements[END_REF]. The results of the validation are shown in Fig. 8, based on equation ( 8) and (19) for 3 expansion terms. For this experimental validation we have just considered a lossless line, being the aim just to verify the possibility of approximating the MTL's TRP through a single-wire equivalent line.

The agreement is quite good, with a maximum error about 1.5 dB with respect to the approximation ξ ∼ = 1, actually being ξ ∼ = 1.02 for the CM; for the other modes ξ i ∈ [1.39, 1.58]. The procedure here proposed could also be used for estimating the line's immunity with respect to an external interference, thanks to the reciprocity theorem [START_REF] Hill | Radiated Emissions and Immunity of Microstrip Transmission Lines: Theory and Reverberation Chamber Measurements[END_REF], assessing the CM current induced along the line. This

VI. CONCLUSIONS AND FURTHER DEVELOPMENTS

We have presented an analytical solution for the TRP for a single-wire line above an ideal ground-plane. The solution, expressed as a series expansion, appears to be fast-convergent, requiring just 3 terms for h/λ < 1/3 (h = 10 cm at 1 GHz). In particular, the solution does not require the line to be electrically short. A two-step procedure has also been envisaged for applying the proposed model to an actual single-wire line, whose validity has been verified through experimental investigation.

Moreover, it has been shown that the proposed formulation can be effectively used for the estimation of the radiated emission/immunity of a unshielded MTL, which is an important feature when dealing with EMC issues in the automotive domain. The extension of the model to non-packed or open MTL is currently in progress, i.e. for a class of lines were the DM's contribution becomes important. Besides, the same procedure we are using for dealing with open MTLs might be used for including the contribution of VRs, at least on a speculative level; unfortunately, in this case a more complex multi-step approach should be envisaged, since the line could be no more regarded as uniform.

Fig. 1 .

 1 Fig. 1. The overhead line.

Fig. 3 .

 3 Fig. 3. A sketch of the setup employed for the experimental validation.

Fig. 4 .

 4 Fig. 4. The simulation results for the TRP of the mock-up line using NEC2 and the proposed model.

Fig. 5 .

 5 Fig. 5. An example of attenuated CD and the equivalent CDs employed by the model.

Fig. 6 .

 6 Fig.6. Some results from the experimental validation of the proposed two-step procedure. The fluctuations in the low-frequency range are due to the limited number of cavity modes for the MSRC.

Fig. 7 .

 7 Fig. 7. The 9-wire test case for the application to an MTL. No VRs are present.

Fig. 8 .

 8 Fig.8. The numerical validation for the 9-wire test case.

VII. ACKNOWLEDGEMENTS

The authors are grateful to Lamine Koné (USTL, Lille, France) for his invaluable support during the experimental validations.