London Roger A Matthews
email: mattherd@lsbu.ac.uk

The Construction of 'So What?' Criminology: A Realist Analysis

From a realist perspective there is a growing body of criminology that can be classified as 'So What?' criminology in that it involves a low level of theorisation, thin, inconsistent or vague concepts and categories, embodies a dubious methodology or has little or no policy relevance. The production of 'So What?' criminology is, of course, no accident but the outcome of a number of lines of force that have served to shape the nature of mainstream academic criminology in recent years. The aim of this article is to identify some of these lines of force and to assess their impact.

Introduction

Over the last twenty years academic criminology has expanded enormously in many western countries involving a proliferation of courses, journals and conferences. At the same time the social and political impact of academic criminology has diminished considerably [START_REF] Currie | Against Marginality: Arguments for A Public Criminology[END_REF]. Increasingly within academic criminology there is a growing body of work that can be designated as "So What?" criminology. That is, there an increasing number of publications that are weak theoretically, employ dubious methodologies or have little or no discernable policy relevance. There are a number of developments that have taken place within the sub-discipline of criminology, that have contributed more or less directly to the spread of "So What?" criminology. These include the growing influence of postmodernism, the demise of critical criminology, the lure of empiricism, a widespread pessimism or impossibilism and the adoption of an instrumentalist approach to what works.

In focussing on these developments and examining their impact on criminological understanding and social policy, the aim is to build upon previous discussions of 'So What?' criminology [START_REF] Matthews | Beyond "So What?" Criminology: Rediscovering Realism[END_REF]. It has been suggested that criminological approaches that ignore class, the state and social structures are unlikely to grasp the fundamental dynamics of the criminal justice system and to comprehend the relations between structure and agency.

It has also been suggested that the ascendancy of administrative criminology and the increasing domination of criminological research by governmental agencies has served to shift the emphasis away from critical theorising towards a more pragmatic approach that typically result in the production of low level equivocal findings. This work, like most forms of pragmatism, often turn out to be of limited practical value [START_REF] Walters | New Modes of Governance and the Commodification of Criminological Knowledge[END_REF]. The other approach that has gained ground in recent years has been liberal criminology in its various forms, which has benefited from the demise of conventional conservative criminology that was influential in the 1980s and which has rapidly declined in significance during the 1990s.

The notion of "So What?" criminology also embraces those studies that employ inadequate or inconsistent categories, present purely descriptive accounts, focus on the trivial or inconsequential or present the material in an unintelligible form. There are also those studies that are purely theoreticist, essentially speculative and opinionated, that use limited and selective evidence as well as those who fail to follow through the implications of their analysis and typically call for more research.

Postmodernism Encounters

Postmodernist thought has not only had a significant impact on social sciences in general but has also deeply influenced criminology in a number of ways. In particular, it is suspicious towards concepts of truth and falsity as well as expressing incredulity towards metanarratives such as philosophical systems or Marxism. In its most damaging forms it expresses a distrust of the idea of knowledge having an emancipatory role and instead claims that knowledge is relative to the beholder or to a particular social group [START_REF] Lyon | Postmodernity[END_REF]. Postmodernism typically advocates an opposition to 'objectivism' and presents an anti-realism.

However, as a number of critics have pointed out, that in presenting the Enlightenment project as an illusion they are themselves presupposing the possibility of reduction of illusion and a better way of life. Moreover, in the process of rejecting 'grand narratives' they invariably construct their own grand narratives and overarching schemas, while veering towards relativism and idealism [START_REF] Callinicos | Against Postmodernism: A Marxist Critique[END_REF][START_REF] Harvey | The Condition of Postmodernity[END_REF].

One of the most influential critiques of the Enlightenment project is Carol Smart's rejection of 'malestream' criminology [START_REF] Smart | Feminist Approaches to Criminology or Postmodern Woman meets Atavistic Man[END_REF]. Smart berates criminology for what she sees as its adoption of grand narratives and argues instead for situated knowledge. Suspicious of what she sees as an essentially male centred criminology, she argues that the truth claims of criminology have to be deconstructed and challenged from a feminist standpoint. Although rightly critiquing situated views of the world that claim to be universal, Smart wants to replace these one-sided and partial views with another set of partial views. As John Lea has argued [START_REF] Lea | Criminology and Postmodernity[END_REF], replacing the views of the dominant group with those of the marginalised, victimised and excluded women is to replace one form of fundamentalism with another. In the end Smart muddies the waters rather than constructing a basis for the development of a feminist criminology. By advocating a form of standpoint feminism together with an anti modernism and anti realism, Smart gravitates towards relativism and foundationalism. From this perspective it is difficult to see how she might develop a policy response that would reduce rape, domestic violence and other crimes that victimise women.

In a similar vein George Pavlich [START_REF] Pavlich | Criticism and Criminology: In Search of Legitimacy[END_REF] clams that realist criminology has compromised critical thinking by 'appealing either to anachronism or to managerial ways of legitimizing its knowledge claim' and becomes a form of pragmatism. Drawing on Lyotard's [START_REF] Lyotard | The Postmodern Condition[END_REF] version of postmodernism he claims that critique itself is in danger of becoming unobtainable and that realists have been drawn into a fundamentally conservative agenda, operating with a dated (i.e. modernist) critical framework. He suggests that the foundations of critical criminology have been eroded and questions whether the word 'critical' continues to have any meaning in the period of 'late modernity'. From this fundamentally defeatist position there is little likelihood of engaging purposefully in the major issues on the social and political agenda and the approach ends up in a form of postmodern defeatism.

Much of the debate about postmodernism in criminology has been submerged in confusion and uncertainty about whether modernist era is over and whether the project of developing reform based on the collection and analysis of data is now outdated. It is also the case that analysing developments in crime control in relation to a supposed transition from modernism to postmodernism has been characterised as being ambiguous and uncertain. While Jonathon Simon [START_REF] Simon | Poor Discipline: Parole and the Social Control of the Underclass, 1890-1990[END_REF],

for example, has argued that emerging penal practices are indicators of a postmodern penality, others have suggested that these developments represent an extension rather than the negation of penal modernism [START_REF] Garland | Penal Modernism and Postmodernism[END_REF][START_REF] Lucken | Contemporary Penal Trends: Modern or Postmodern?[END_REF]. In contrast, Nancy Fraser [START_REF] Fraser | From Discipline to Flexibilization? Re-Reading Foucault in the Shadow of Globalization[END_REF]has argued that it is more appropriate to see developments in social regulation not so much in relation to a transition from modernity to late modernity or postmodernity, but rather in terms of the transition from Fordism to Postfordism. She argues that the nature of disciplinary regimes changed with the transition to Fordism and the concomitant rise of the 'welfare sanction'. Fordism is a totalising system of production, Fraser argues, that instigated a distinctly different mode of regulation based on individual self control ', which fosters their autonomy as a means to their control'. In the era of Postfordist globalisation, however, regulation is becoming decentred and as Giles Deleuze [START_REF] Deleuze | Negotiations[END_REF] has suggested increasingly deinstitutionalised. In this transition to Postfordism the forms of hierarchical discipline which Foucault detailed so effectively in Discipline and Punish (1977) are increasingly being superseded by a post Keynesian, privatised system of control which is multi-layered resulting in what Adam Crawford [START_REF] Crawford | Networked Governance and the Post-Regulatory State[END_REF] has referred to as 'networked governance' or what Nancy Fraser [START_REF] Fraser | From Discipline to Flexibilization? Re-Reading Foucault in the Shadow of Globalization[END_REF] calls 'segmented governmentality'. In Postfordism risk management replaces social insurance and the emphasis is increasingly placed on the care of the self in which 'individuals become increasingly responsible for managing their own human capital to maximum effect'. The implication of this form of analysis is that it is more productive to analyse the changing forms of crime control in terms of the transition to Postfordist modes of regulation rather than in terms of the rather nebulous concept of 'late modernity'.

Although there is a need to analyse changes in the nature of discipline and social control within a wider a wider analytic framework incorporating some consideration of changes in productive relations, it remains the case, however, that critical realism is tied to the Enlightenment project in as much as it believes in that the pursuit of progressive social change should be based on reliable evidence and analysis. Thus, rather than see postmodernism as the rejection of the modernist project, realists are more sympathetic to Zygmunt Bauman's [START_REF] Bauman | Life in Fragments: Essays in Postmodern Morality[END_REF] conception of postmodernism as modernity coming to terms with its own limitations. The realisation that the modernist project was inherently contradictory does not detract from the objective of using knowledge to effect social reform.

The Demise of Critical Criminology

It is all too easy to forget just how powerful and influential critical and radical criminology was in the 1970s in the form of new deviancy theory, labelling theory, subcultural theory and neo-Marxist criminologies. The dominant conceptions of 'inclusion' and 'exclusion', 'normal' and the 'pathological' were called into question and the taken-for-granted nature of 'crime' was repeatedly problematised. These critiques destabilised the hegemonic domination of 'conventional' and 'positivist' criminologies and challenged the categories on which their analyses had been based. Importantly, critical criminology encouraged debates about values, meanings, power and politics [START_REF] Ferrell | Cultural Criminology[END_REF]. This opened the door for a release from the straightjacket of rigid and unreflexive categories and from the limited utility of natural scientific methods in criminology.

In many respects this critical input turned conventional criminology on its head. The delinquent became the normal in search of kicks and relief from boredom. Crime and deviance were seen as being the product of social reaction and by implication socially constructed. During much of the 1970s critical criminology made considerable ground, but during the following decade it became increasingly subject to criticism from a number of directions. It was accused of idealism, the romanticisation of the deviant, relativism and ultimately inverting rather than transcending the limitations of conventional criminology [START_REF] Young | Working Class Criminology[END_REF]. Most significantly, it was argued, the mode of critique was largely negative and dismissive rather than engaged and constructive [START_REF] Cohen | Against Criminology[END_REF].

In essence, critical criminology failed to develop a credible alternative vision, or a perspective that could provide a sustained critique of conventional criminology while effectively engaging in the business of practical social reform. [START_REF] Van Swaaningen | Reclaiming Critical Criminology: Social Justice and the European Tradition[END_REF]. The demise of the National Deviancy Conference in 1975 and the absorption of the critical criminology group within the American Society of Criminology some years later signalled the failure of critical criminology to remain independent of the mainstream and instead became the 'bad conscience' of conventional criminology.

The collapse of communism in Russia in the 1980s and the evaporation of the associated socialist vision in the west, suggested that capitalism would not wither away and therefore crime and inequality would, in some form, be with us for the foreseeable future. This transformation of structures and political visions raised nagging issues about freedom, justice, and culpability, which few critical criminologists seriously confronted. For the most part critical criminologists adopted a liberal notion of individual freedom from state interference and became both anti-statist and in many cases anti-punishment. The consequence of this was that there was a general tendency to argue for less state 'interference', reduced levels of punishment and incarceration, greater use of 'alternatives' and welfare orientated incentives designed to support, educate and manage 'deviants' rather than punish them [START_REF] Cohen | Against Criminology[END_REF]. One of the notable exceptions to this liberal vision was presented by John Braithwaite and Philip Pettit [START_REF] Braithwaite | Not Just Deserts: A Republican Theory of Criminal Justice[END_REF] , who attempted to address the questions of why punish, who to punish and what form of punishment is appropriate for which type of offender.

A great deal of critical criminology satisfied itself with ideology critique.

The aim being to show that certain beliefs are false, with the aim of reducing illusion. However, less common were attempts to show why such beliefs are held and what produces them. Relatively few critiques identify the material conditions on which such illusions are based. As Marx demonstrated, it is one of the characteristics of the capitalist mode of production that it routinely generates representations in distorted and inverted forms. If we are to move beyond ideology critique and expose criminology we need to know exactly how the removal of these illusions and distortions could be achieved.

Critical criminologists for a number of reasons were generally reluctant to spell out alternative visions or provide futuristic 'blueprints'. Consequently many critical criminologists during the 1970s and 1980s took refuge under the Thomas Mathiesen notion of the 'unfinished' and found some solace in the views that presenting detailed blueprints of social change was likely to either involve a series of practical traps or engage the reformer in collusion and the dilution of objectives.

Although there is element of truth in Mathiesen's position since although we may be able to identify the causes of social ills we may not in the immediate future be able to see a way of eliminating these causes without generating greater problems. The difficulty arises, however, that if no feasible or desirable alternative is offered the force of critique is weakened and the possibility of mobilising support for reform is diminished. Alternatively, some critical criminologists have responded to the perceived inability to construct a viable programme of criminal justice reforms by embracing forms of anti-criminology, which provides a rationale for not engaging in criminal justice reform while paradoxically remaining in the criminological camp [START_REF] Cohen | Against Criminology[END_REF][START_REF]Beyond Criminology: Taking Harm Seriously[END_REF].

A more promising attempt to resurrect critical criminology has come in recent years from cultural criminology [START_REF] Ferrell | Cultural Criminology[END_REF][START_REF] Ferrell | Cultural Criminology[END_REF]. Cultural criminologists have injected a much needed vitality back into the subject through their engagement with the lived experience of deviant and marginalised groups. The emphasis on meaning and interpretation has provided an important antidote to the dry and uninspiring contributions of administrative and positivistic criminologies. But there are issues about meaning and analysis of the key term 'culture' since the term can have a number of different meanings -value systems, social norms, traditions, folkways, habits and the like [START_REF] Garland | Concepts of Culture in the Sociology Punishment[END_REF][START_REF] O'brien | What is Cultural About Cultural Criminology?[END_REF]. Depending on which notion of culture is adopted there are related issues that arise concerning the appropriate form of analysis.

Although cultural criminology claims to offer a 'ruthless cultural criticism of everything existing', it shares with much conventional criminology and postmodernism a disdain of political economy, social structures, the state, grand narratives and instead gravitates towards situational and micro-analysis [START_REF] Ferrell | For a Ruthless Cultural Criticism of Everything Existing[END_REF][START_REF] Ferrell | Edgework, Media Practices and the Elongation of Meaning[END_REF][START_REF] Hall | Cultural Criminology and Primitive Accumulation: A Formal Introduction to Two Strangers Who Really Should Become More Intimate[END_REF]. Indicatively, it has little purchase on the more serious forms of crimeviolence, homicide, rape and sexual offences. Moreover, it is difficult to see these offences can be properly understood in terms of resistance, edgework or as a function of media influences, or so called moral panics.

At the same time, there is a tendency in some of the contributions to cultural criminology to present capitalism as an essentially negative, repressive and destructive force, while 'deviants' and 'criminals' are for the most part seen to be engaged in acts of justified resistance. Crime on the other hand is in danger of being reduced to a series of representations or discourses or seen as a form of drama or carnival [START_REF] Presdee | Cultural Criminology and the Carnival of Crime[END_REF]. Consequently there is little appreciation of the positive and contradictory dynamics of capitalist accumulation and how these shape or condition cultural processes, or for that matter how cultural process contribute and influence the complexities of capitalist development.

The separation of the cultural from issues of political economy tends to produce a rarefied conception of culture. There is also a tendency in some of the contributions to cultural criminology of treating culture as if it were a unified phenomena rather than a set of competing norms and values. Indeed, it may well be the case that just as the notion of community became the focus of sociological attention at the point when traditional communities were breaking down or disappearing, so it seems that critical criminologists have come to focus on cultural activities at appoint at which 'culture' is becoming more diverse, fragmented and contested. It may also be the case that the attraction of cultural criminology may be less to do with its contribution to progressive politics, but rather its tendency to downplay the nature and impact of crime and focus on 'deviancy' and low-level transgressions in a period of a rapid crime drop, and in a context in which crime itself is sliding down the social and political agenda [START_REF] Jacobson | Downsizing Prisons: How to Reduce Crime and End Mass Incarceration[END_REF]. On the other hand, the crime drop itself may be a function of as yet largely unexamined cultural shifts [START_REF] Blumstein | The Crime Drop in America[END_REF][START_REF] Karmen | The New York Murder Mystery[END_REF].

The promise of cultural criminology is yet be realised but there is a concern that like previous versions of critical criminology that rather than confronting and seriously challenging the hegemony of conventional criminology that it becomes absorbed in within the mainstream providing more of a change of emphasis rather than a change of direction. The lack of clarity about the nature of its object of investigation -culture -and of the appropriate methods to study, it presents an eclectic and uncoordinated set of approaches that lack an identifiable political focus.

However, developing an overtly critical approach to criminology remains an important objective if we are to explore the emancipatory potential of the subject.

Picking up the critical baton that criminology requires, it has been suggested, calls for an engaged approach that goes beyond ideology critique and 'the unfinished' to the identification of viable alternatives, together with strategies and visions of how these alternatives could be realised. From a realist perspective if cultural criminology is to be worthwhile, it needs to be critical of its object. It also needs to avoid cultural reductionism and rather than reducing considerations of political economy into the 'lifeworlds' or seeing capitalism in exclusively negative terms, it needs to recognise that cultural forms contain progressive as well as destructive elements and that part of the debate is making distinctions between contradictory and competing cultural forms [START_REF] Maclennan | Cultural Studies: Towards a Realist Intervention[END_REF][START_REF] Ray | Culture and Economy After the Cultural Turn[END_REF].

The Lure of Empiricism

The problem of method in social science has centred around the opposition between deductivism and inductivism and correspondingly between realism and empiricism. Empiricism, or positivism, in the philosophy of science is broadly speaking the view that scientific investigation can be confined to observable phenomena and their formal relations, while realism embodies the view that there is a reality independent of our knowledge of it and that this reality is stratified containing emergent properties whose effects should not be conflated with our experience of them [START_REF] Bhaskar | A Realist Theory of Science[END_REF][START_REF] Dilworth | Empiricism vs. Realism: High Points in the Debate During the Past 150 Years[END_REF]. Whereas empiricism is inductive and believes that 'facts speak for themselves' and that theories can be constructed by gathering and sifting of data, realists believe that social scientific investigation should be theory led and that it is our theories and concepts that serve to carve up the world and make sense of the multitude of 'facts' that comprise the real world [START_REF] Manicas | A Realist Philosophy of Social Sciences[END_REF].

For the most part empiricists emulate the methods of the natural sciences and frequently claim that their endeavours are 'scientific', whereas realism maintains that social scientific investigation necessarily involves the interpretation of human meaning, intentions and actions, and therefore requires a range of methods, the choice of which will be dependent on the nature of object under study and what one wants to learn about it. Realists argue that because social systems are always open and usually quite complex and messy, it is very difficult if not impossible to isolate the components that we want to examine under controlled conditions as may occur in the natural sciences [START_REF] Sayer | Critical Realism and the Limits to Critical Social Science[END_REF][START_REF] Sayer | Realism and Social Science[END_REF].

As C. Wright Mills argues in The Sociological Imagination (1959) abstracted empiricism tends to be a-theoretical with little conception of the historical and social forces that shape both natural and social scientific investigation. Indeed, where structural and historical factors are used in empiricist studies they are often 'above' the level of the data made available in the research, or alternatively refer to psychological factors that operate 'below' the level of data presented. Typically when literature reviews are conducted Mills suggests it is not to develop a theory, test assumptions or to give the study meaning but in many cases the literature review is presented independently of the research report and is often written up after the data is collected. Empiricism, however, can take a number of forms, some of which are more subtle than the usual form of abstracted empiricism. For example, a popular strategy in criminology is to take two phenomena that appear to be changing simultaneously in related ways and to claim that one must be causing the changes in the other. Identifying these forms of correspondence has become a major preoccupation for criminologists, even amongst those who have radical pretensions. One of the most influential representatives of this form of empiricism is Loic Wacquant [START_REF] Wacquant | The New Peculiar Institution: On the Prison as a Surrogate Ghetto[END_REF][START_REF] Wacquant | The Great Penal Leap Backwards: Incarceration in America from Nixon to Clinton[END_REF] who has presented a number of explanations of the changing nature of crime control on the basis of observing two phenomena changing simultaneously. Thus he observes the decline of the ghetto in the US and the expansion of the prison, and concludes that the prison must be replacing the ghetto. In a similar vein he sees the demise of the Keynesian welfare state and the simultaneous growth of the prison and concludes that they must be functionally related. In addition, he claims that the rise of the prison population in the US is a function of the rise of neo-liberalism and postmodern insecurity, despite the fact that the number of people prisons has decreased in periods of neo-liberalism (as occurred in the Thatcher era) and seems impervious to the fact that neo-liberals are generally interested in minimal statism rather than expanding state provision, particularly in the very expensive form of incarceration.

It is also the case that he widespread claim of criminologists that we are experiencing a surge of 'populist punitiveness' fails to recognise that there is no automatic relation between changing forms of political economy, cultural forms and political structures that that leads directly or inevitably towards the formation of punitive sensibilities. Taking the same logic it might be expected that in a period of rapid social and economic change involving the fragmentation of communities, growing inequalities and the breakdown of informal controls that crime would rise significantly. However, the opposite has occurred. This may well be because the sensibilities and identities in the Postfordist era require not so much an emphasis on toughness and rigidity as on flexibility and ambivalence [START_REF] Bauman | Life in Fragments: Essays in Postmodern Morality[END_REF][START_REF] Sennett | The Corrosion of Character: The Personal Consequences of Work in the New Capitalism[END_REF]. In modern parlance the key terms are 'being cool' and 'having respect'. It is relation to flexibility -personal and social and economic -that people are judged and valued in contemporary society, whereas punitiveness is more likely to be seen as 'uncool' and as an indicator of rigidity.

In the same way there is little evidence of declining welfare budgets in most advanced western countries that have expanding prison populations and that even in the US states such as California significantly increased welfare expenditure in the 1990s as prison populations were expanding [START_REF] Greenberg | Novus Ordo Saeclorum? A Commentary on Downes and Beckett and Western[END_REF]. It would seem that it is not so much a question of a reduction in welfare expenditure per se, but of the reorganisation and redistribution of welfare. The attractiveness of this form of functionalist empiricism is not difficult to understand for those who want simplistic answers to complex issues. These types of accounts are superficially attractive, but the complex ways in which these phenomena may be connected are not explored, and it is the regularity of their appearance that provides the (questionable) basis of explanation. However, as critical realists argue, what causes something to happen has nothing to do with the number of times that we have observed it happening [START_REF] Sayer | Realism and Social Science[END_REF][START_REF] Pawson | Evidence-Based Policy: A Realist Perspective[END_REF].

Another prevalent example of empiricism involves what we might call inverted empiricism. This is the approach that assumes that because we cannot observe regular corresponding changes in two phenomena they cannot be causally related. This type of empiricism is evident in the majority of studies in criminology on the relationship between crime rates and the prison population. Since imprisonment rates have increased significantly over the last decade or so in the UK and in America, while the recorded crime rates have fallen, it is frequently concluded that there is no discernable causal link between the crime rate and imprisonment rate. Thus Michael Tonry, for example, in his book Penal reform in Overcrowded Times can assert in a section entitled 'crude empiricism' that the 'explanation for why so many Americans are in prison, that our crime rates are higher or faster rising than in other countries, has virtually no validity' [69:54].

Having made this statement he draws on the International Crime Victimisation

Survey, which is one of the crudest examples of criminological empiricism, to show that the chances of being burgled in the US are lower than most European countries, although he concedes that violent crime is much higher in the US than most other countries. Thus in an impressive piece of logic, Tonry, who is seen as one of the leading international experts on punishment and imprisonment concludes his discussion on 'crude empiricism' with the startling and unverified claim that: "American imprisonment rates rose because American politicians wanted them to rise." [69:57]. Thus the complex dynamics of prison expansion are reduced to a form of voluntarism. However, it makes little sense to compare changes in the overall recorded crime rate and the imprisonment rate since a large percentage of recorded crimes are unlikely to warrant a prison sentence. To better understand the connection we need to examine the process of attrition, particularly for those offences that are highly likely to end in a prison sentence if the offender is found guilty and to examine the forms of decision-making at various points in the criminal justice system, particularly by the police and sentencers. The causal connections between different types of crime may be indirect, heavily mediated and subject to an array of different forces and forms of decision-making, but it does not mean that causal connections cannot be identified [START_REF] Matthews | Doing Time: An Introduction to the Sociology of Imprisonment[END_REF].

If we look, for example, at the growth of women's imprisonment over the past decade or so in different countries such as America, Canada, Australia and England and Wales there does seem to be a causal connection between the growing number of women prosecuted and convicted of various crimes, particularly violence and the growth of women's imprisonment [START_REF] Gelb | Women in Prison -Why the Rate of Incarceration is Increasing[END_REF][START_REF] Kong | Female Offenders in Canada[END_REF][START_REF] Sabol | Prisoners in America[END_REF]]. It may be the case as Meda Chesney-Lind [START_REF] Chesney-Lind | Patriarchy, Crime and Justice: Feminist Criminology in an Era of Backlash[END_REF] has argued that this may be a function to some extent of a redefining and re-categorisation of women's actions but there can be little doubt that the growing number of convictions and prosecutions for relatively serious crimes his causally related to the growing number of women incarcerated in these countries. The problem as always is that there are a number of causal processes in play with different, and at times contrasting, impacts. Our aim however, should not be to engage in a fruitless and meaningless form of inverted empiricism but instead to identify the causal mechanisms which shape and produce the outcomes that we are examining. Moreover, the denial of any meaningful relation between recorded crime rates and imprisonment is one of the major conceptual fault lines that runs through criminology, creating almost two distinct sub-disciplines of 'crime' and 'punishment' that are studied independently from each other, with the consequence that punishment tends to appear arbitrary. This in turn makes informed and normative discussions of punishment and imprisonment extremely difficult and at the same time tends to disconnect academic criminologists from the concerns of the public and policy makers.

Thus in order to avoid the excess of voluntarism and reductionism realists place considerable emphasis on causal explanations. The main objective is to distinguish the causal from the contingent. Rather than engage in empiricism with its interest in statistical correlations and recurring events, or be satisfied with pure descriptions, realists are concerned with the question of 'why' change occurs and in identifying the causal dynamics that produce non-random outcomes.

Pessimism and Impossibilism

A general reading of recent criminological literature could reasonably lead one to the conclusion that many criminologists believe that things are getting worse. Growing public anxieties, increased prison populations, tougher policing, and in general belief that are living under a dark cloud of 'populist punitiveness' are the types of messages that criminologists like to deliver [START_REF] Ericson | Crime in an Insecure World[END_REF][START_REF] Pratt | The New Punitiveness: Trends, Theories, Perspectives[END_REF][START_REF] Simon | Entitlement to Cruelty; Neo-Liberalism and the Punitive Mentality in the United States[END_REF]. Thus, many criminologists see themselves as disseminators of bad news and there can be little doubt that a considerable number of criminologists are most comfortable when presenting dystopic visions [START_REF] Hutchinson | Countering Catastrophic Criminology[END_REF][START_REF] Zedner | Dangers of Dystopias in Penal Theory[END_REF].

In conjunction with this widespread pessimism there is a cynicism that claims explicitly or implicitly that interventions do not or cannot work and whenever any new policy initiatives are developed these cynics they feel obliged to give a list of reasons why they will not work. In very few cases do these pessimists explain what might work and instead prefer to occupy the safer terrain of noninterventionism. Let us take an example of pessimism -the project of penal reform. There is a widespread consensus amongst academic criminologists that prisons consistently fail in terms of their designated goals of reforming offenders or reducing crime, or increasing public safety. The dominant response to the perceived 'failure' of imprisonment is either reductionism or abolitionism. Although there are a number of different penal reform strategies available such as changing sentencing policy, privatisation, modifying regimes and staff-inmate relations the strategies of penal reform boil down essentially to a choice between reductionism and abolitionism [START_REF] Hough | Tackling Prison Overcrowding[END_REF][START_REF] Jacobson | Downsizing Prisons: How to Reduce Crime and End Mass Incarceration[END_REF].

The mantra of reductionism is that there are, by definition, too many people in prison and the objective is to reduce the number. However, reductionists are very uncertain about the degree of reduction that should take place and by implication, how many people should be in prison. The logic of reductionism is that however many people there are in prison it is always going to be too many.

The favoured strategy for reducing the prison population amongst reductionists is developing community based 'alternatives'. However, the research shows that 'alternatives' tend to involve net widening and that rather than reduce the level of imprisonment they help to create an expanded network of criminal justice and related agencies that provide a systematic form of recruitment and referral into the prison system [START_REF] Cohen | Visions of Social Control[END_REF].

Abolitionists on the other hand, partly in response to the perceived limitations of reductionism and reformism, argue that some or all groups of offenders should be ineligible for imprisonment and that custodial institutions should be closed down and phased out [START_REF] Sim | Punishment and Prisons: Power and the Carceral State[END_REF]. One of the leading abolitionists, Pat Carlen [START_REF] Carlen | Carceral Clawback: The Case of Women's Imprisonment in Canada[END_REF], has argued for a gender based abolitionist strategy such that women convicted of the same offence as men would, apart from a few exceptional cases, not be subject to incarceration. She argues that penal reform is either ineffective or counterproductive and has coined the term 'carceral clawback', which refers to the process by which certain gains made through reforms are seen to be countered by other managerial or organisational imperatives. A survey of her writings on penal reform represents a very pessimistic vision. In general her approach can be summarised in the following form:

• However much you improve conditions, a 'prison is a prison' which deprives people of their liberty • There is always a mismatch between intentions and outcomes, and therefore reform is always likely to fail • You may change or improve certain aspects of incarceration but the overarching structure remains intact • There may be some improvements, but you could have done something else that could have been better

These arguments against reformism have, of course, been applied to other areas.

The underlying argument is that if you do manage to improve conditions that you just relegitimise the prison or the criminal justice system and reinforce and extend its powers. On the other hand, if you do not improve conditions the offenders will become more damaged and more marginalised which will make them more prone to offending. This 'no win' scenario is a regular feature of the writings of liberal pessimists and provides a major obstacle to the development of constructive and progressive reforms in different areas of criminal justice. Indeed, it is possible to trace a line of pessimism that runs through postmodern defeatism, the more negative forms of critical criminology and amongst liberal pessimists.

What Works?

Over the past twenty years or so the dominant ideology in criminology has shifted from a 'nothing works' position to a focus on 'what works' [START_REF] Cullen | From Nothing Works to What Works: Changing professional Ideology in the 21 st[END_REF].

Developing an evidence based approach criminologists have attempted to overcome the nihilism of the 'nothing works' era with the systematic marshalling of evidence in order to produce more viable and effective policies. Although there has been something of a welcome break with the pessimism and impossibilism of the 'nothing works' position, the new focus on finding out what works has been less impressive than was generally expected. This is largely because the strategies employed to find out what works have been typically theoretically weak and/or methodologically inadequate and operated with a largely instrumentalist conception of what works.

One example of the development of an evidence based approach to what works has centred around the adoption of the 'experimental paradigm' advocated by Donald Campbell and his associates, which attempt to design social research in a manner that emulates the rules and precepts of natural scientific investigation, particularly in line with those adopted in medicine and health care [START_REF] Cook | Quasi-Experimentation[END_REF]. Although the Campbell group aim to develop an evidence based approach to policy, the application of their scientific approach to the complex 'open systems' of the social world has proved to be less than adequate [START_REF] Tilley | Evaluation and Evidence -Led Crime Reduction and Policy[END_REF]. Similarly, the use of random control trials in which there is normally an experimental group which is subject to 'treatment' and a control group which is not, such that any difference in the change between the experimental group and the control group is seen to be attributable to the intervention, have also been shown to have serious limitations. These studies can often produce mixed findings, while it is rarely acknowledged that the intervention itself may more or less directly affect the outcomes.

Most significantly, the problem is that the same measure may work in different ways in different settings and have different effects according to variations in the circumstances of those involved. Thus instead of boldly claiming that certain interventions (always) 'work', it may be more appropriate and more realistic to claim that certain interventions work for some people in some conditions some of the time.

One instructive example of the limitations of recent government funded research, which aims to provide evidence based policy, is a reducing burglary initiative conducted by a consortium in the UK. In this research the original finding was that the initiative had limited impact. However the data was reworked by the Home Office to show an improvement in the outcomes, claiming a 25 per cent drop in burglary Thus the conclusion of this work was that if an intervention does not in fact work, that rather than find out why it did not work, the preferred official response in this case at least is, as Tim Hope has argued, to 'pretend it works' [START_REF] Hope | Pretend it Works: Evidence and Governance in the Evaluation of the Reducing Burglary Initiative[END_REF].

A further example of the limits of attempts to establish 'what works' is the assessments of Cognitive Behavioural Programmes (CBT). Recent research by the Home Office and the Youth Justice Board claim that CBT can be effective in reducing reoffending [START_REF] Cann | Cognitive Skills Programmes: Impact on Reducing Reconviction Among a Sample of Female Prisoners[END_REF]. However, the research carried out by the Home Office indicate that such programmes rarely 'work' as intended and that dropout rates are very high and that in those rare instances where there is an improvement in reconviction rates following an intervention, John Pitts [START_REF] Pitts | Who Cares What Works?[END_REF] has argued that it is not clear for whom it has worked or why it has worked.

Also in relation to Cognitive Behavioural Therapy (CBT) Pawson and Tilley

[54] demonstrate that the selection of the different groups on which CBT is exercised skews the results and they conclude in their review of the evidence that the group which demonstrated the greatest success were those who were eligible for CBT but did not participate in the programme. These errors and omissions, which severely detract from the reliability of the research, have not prevented the widespread adoption of these programmes by governments and prison departments. The important point that Pawson and Tilley make in relation to these programmes is that they cannot be evaluated without some appreciation of the population to which they are directed and the context in which they takes place.

The implication is that very few interventions work for all subjects in all contexts, and that it is not that interventions 'work' unconditionally, but that they 'work' to the extent that they connect with the capacities, aspirations and interests of those to whom they are directed. Those interests and capacities will in turn be conditioned by the context in which the interventions occur. Just as the capacity of gun powder to explode is conditioned by the context (i.e. whether it is wet or dry) in which it is placed, the capacity of interventions to 'fire' will be dependent on the context in which they are deployed. Since it is usually a multiplicity of causes that produce one event rather than a single cause, the challenge is to identify the generative causal connections and to discount contingent connections. Answering this question requires systematic empirical investigation.

In contrast to the instrumentalist view of 'what works', critical realists operate with a different view of intervention and its effects. Interventions are not so much concerned with applying known remedies to problematic situations but implementing theories about what might work. Interventions involve a number of different stages and will be applied in different ways in different contexts.

Ray Pawson [53] has argued that the influence of research in policy often occurs through the medium of ideas rather than that of data. That is, it is not so much the discovery of an impressive 'fact' that changes the course of policy making, rather research contributes to the clash of ideas and 'the key to enlightenment is to insinuate research results into this reckoning'. Thus it is the explanations not the numerical results from reviews and research that speak directly to the choices that have to be made in devising or reforming a programme. Thus: "Policy-makers are likely to struggle with data that reveal for instance, the respective significance of an array of mediators and moderators in metaanalysis. They are more likely to be able to interpret and to utilise a fullblown realist explanation of why a programme theory works better in one context than another. Although these two investigatory thoughts serve to answer rather similar questions, the one that focuses on sense making has the advantage. This is especially so if the investigation focuses on adjudicating between rival explanations, thus providing the justification for taking one course of action rather than another. This is the very stuff of political decision-making." [53:169].

Conclusion

This article is to some extent guilty of the charges laid against the pessimists by dwelling on the negative developments in academic criminology. However, if we are to develop a more critical and engaged form of criminological investigation there is a considerable amount of path clearing and rethinking that needs to be undertaken.

It has been suggested that the demise of critical criminology has facilitated the drift back towards the adoption of natural scientific approaches employing inappropriate methods to study social phenomena. In the process not only has criminology lost much of its critical edge, but also increasingly operates with taken-for-granted commonsensical categories of crime. At the same time there has been a decrease in overt forms of overt political commitment and normative theorising.

The ascendancy of administrative criminology, which is notably light on theory and adopts undeconstructed commonsense categories, is ultimately of limited utility. In opposition to these approaches there is a need to build on the renewed vitality of critical criminology which has been generated by cultural criminologists, that is able to produce an engaged, progressive political approach, that is based on rigorous methodology and that can integrate the study of 'culture' in a non reductionist manner. Thus one of the immediate tasks of 'cultural realism' is to integrate the work of cultural criminologists into a left social democratic programme that can provide the normative and political vantage point on which to base research programmes and develop progressive interventions.

The development of such a programme would help to counter the deepseated pessimism and impossibilism that runs through criminology. Doing nothing or trying to find reasons why proposed interventions are destined to fail creates a form of disengagement that allows policy makers and politicians a relatively free hand to orchestrate criminal justice policy. These issues, however, are too important to be left to politicians and policy makers alone. Although pessimism and impossibilism are a long-standing feature of criminology, the recent wave of postmodernism has exacerbated these tendencies by advocating forms of relativism and defeatism. In opposition, critical realism remains tied to a modernist problematic and to the process of social reform through the collection of evidence based on sound methodologies.

Finally, it is interesting to note that in the UK academic production in the future is to be evaluated not solely in terms of the number of citations and publications but increasingly in relation to their 'impact'. Although there are considerable difficulties in determining exactly how 'impact' is to be measured and assessed, this development does potentially represent a positive initiative in that it may encourage academics to make their work more policy relevant. However, if

  Despite warnings from C. Wright Mills and other major sociologists, empiricism and positivism remain prevalent in social science in general and criminology in particular. The growing body of government sponsored administrative criminology represents one of the most prominent examples of empiricism. Typically light in theory and heavy on statistical manipulation, these studies collect data on different aspects of crime, victimisation and the operation of the criminal justice system such that much of this work is often small scale, localised and descriptive producing equivocal conclusions. A major limitation of these studies is that they make little contribution to the development of cumulative knowledge and theory building.

these contributions to policy and practice are to be positive some serious consideration needs to be given to the use of the concepts and categories that frame research and to the methodologies and forms of analysis that are adopted.


D Mihailova

J Van Dijk

M Grozeva

G Degrez

J J A M Van Der Mullen

Towards a reduced chemistry module of a He-Ar-Cu hollow cathode discharge

This study is aimed to find a reduced chemistry module for hollow cathode discharge excited in a He-Ar-Cu mixture. This enables to construct lean and realible models that can be used as a part of the design tool of hollow cathode discharges (HCDs). To this end estimative calculations and numerical simulations are performed at optimal conditions for lasing. An analysis of the species behaviour and reactions is made and as a result the model is simplified by means of reducing the number of species and reactions. The consequences of these reductions is justified by comparing the results of the simplified models with those of a more complete one. This study delivers a model that is chemical lean and thus, much less time consuming. It can be used in optimization studies to find the optimum in the plasma control parameter-set of HCDs. The technique developed in this study for HCDs can be applied to glow discharges in general.

Introduction

The interest in complex chemistry plasmas is increasing rapidly during the last decade. This is among others boosted by the booming attention paid to plasmas for biomedical applications and environmental technology. In all these modern applications the classical atomic plasma composed of one single noble gas species is replaced by plasmas created in rich chemical fillings. As a consequence of plasma activities these filling are transformed into a myriad of excited atoms, molecules, radicals and various types of ions. This gives firm ground to the statement that the problem of plasma physics nowadays mostly lies in plasma chemistry.

One of the serious problems is manifested by the increase in the number N of relevant species. For a complex plasma this can easily go beyond N = 100. Even more seriously is the number of conversion reactions between these species for which we can expect a scaling with something like N 2 . A further complicating factor is the large variety in reaction speeds. Here we can easily find differences in the order of 10 3 . This makes that complex chemistry plasma models can become extremely stiff.

In search for the most appropriate strategy to model these plasmas the question rises whether it is really needed to treat all the species individually. Should we compute for all the species their densities and transport fluxes? Or, do there exist systematic methods that can lead to a reduced chemistry? A reduced chemistry module is a module that is small enough to make the grand plasma model lean while the computation of the main plasma properties is not in jeopardy.

This study is devoted to the search of a reduced chemistry module for hollow cathode discharges (HCDs) used for laser applications. Such a module enables to construct a lean and reliable model that can be used as part of a design tool of HCD lasers. The aim of this tool is to find, by modelling, the optimum in the plasma control parameters-set of these plasmas. Since the control parameter space is enormous it is requested that the model converges easily so that the exploration of this hyper-space is not too much time consuming. With this chemical lean model it is then possible to find the best version of the geometrical construction, the anode-cathode patterns, the current settings, the fill-chemistry, etc.

This study starts with a model that describes a longitudinal sputtering HCD used for laser application. It has a cylindrical geometry with two anodes at both sides as described in detail in [1,2]. The hollow cathode metal cylinder is with a length of 50 mm and an inner diameter of 4 mm . The sputtered cathode material is Cu and the operating gas is a mixture of He with 5% of Ar. The total gas pressure equals 2.3 kPa and the discharge is excited by a 3 ms current pulse.

The model used for this study is the time-dependent fluid model MD2D described in detail in [2]. The simulation model is based on a set of 10 species and 23 reactions. For these active species the balance equations are solved each of them describing the competition between the transport and chemistry on a per-species base. The results of the simulation includes the spatial and temporal evolution of densities, the reaction rates and transport fluxes of the relevant species. These are used to get volume-averaged values of these quantities. From this output a detailed analysis of the contribution of production/destruction and transport for each species can be obtained so that the most important species and the relevant conversion channels can be determined. The insight obtained can subsequently be used to construct a grand model based on a reduced chemistry. To justify the possible consequences of the chemistry reduction we will compare the results of the simplified models with those of the initial more complex chemistry model. These steps will allow to define the validity range of this reduction method and its applicability to other plasma sources.

The paper is organised as follows: in section 2 the hierarchy in processes is explored and estimative calculations are made. Section 3 describes the set of species and reactions used in the numerical model. A detailed analysis is made and presented in section 4. Based on this analysis simplified models are constructed and the comparison with the more complete model is presented in subsections. Finally, section 5 summarises the observations.

Hierarchy in processes

The analysis of the hierarchy of chemical species and conversion processes will be guided by the general form of the particle balance showing the competition between chemistry (production and destruction processes) and transport. For the particle p it reads:

∂n p ∂t + ∇ • Γ p = S p , (1)
where Γ p is the flux density and S p is net source term. The time-derivative can be omitted since the duration of the excitation current pulse, being 3 ms , greatly exceeds the time-scales of the plasma processes. This implies that steady state (SS) is obtained during the pulse. Omitting the transient term, the continuity equation reads:

∇ • Γ p = S p . (2)
We start with an exploration of the left hand side, the transport side, of this equation. After that the right hand side will be dealt with.

By writing the transport term as ∇ • Γ p = n p ν p t , we introduce the transport frequency ν p t of species p. The flux density Γ p is given by:

Γ p = µ p En p -D p ∇n p , (3)
where the mobility µ p and diffusion coefficient D p of species p are determined by collisions of these species with buffer gas atoms. We see that in general two driving forces are present: the drift generated by the electric field and the diffusion set up by gradients. It is clear that neutral particles are driven by the diffusion only. Due to the additional drift term, the ions will have higher velocities in general. We will come back to this later. The right hand side of equation ( 2), the source term S p is determined by the reactions occurring in the discharge:

S p = c p,r R r , (4)
where c p,r is the net stoichiometric number of particles of species p created in one reaction r while R r is the corresponding reaction rate. The sum runs over all the reactions. The source term S p consists of positive c p,r > 0 (production) and negative c p,r < 0 (loss) contributions. So that it can be split in two terms -the production P p and loss rate L p :

S p = P p -L p . (5)
Note that P p is the total production rate: it is a sum over all the reactions in which p is created. The same applies for the loss rate L p : it is the total loss due to radiative and collision-induced transitions. The production rate can be written as:

P p = r n q D q,p , (6)
where D q,p is the frequency of the destruction processes of particle q that lead to the production of p. The sum runs over all the reactions that lead to the production of p. The destruction of the same level p is:

L p = n p D p , (7)
where D p = r D p,r is the destruction frequency of particle p, the so-called destruction factor of p. Thus, we can write the general form of the particle balance as:

n p ν p t = P p -n p D p (8)
n p ν p t D p = P p D p -n p . (9)
In the case that the transport frequency ν p t is much smaller than the destruction frequency, i.e.

νp t Dp 1, equation ( 9) becomes:

n p = P p D p . ( 10
)
So that the density of p is completely determined by local reactions. The species will be designated by local chemistry (LC) species. Combining equations ( 10) and ( 7) leads to the criteria that holds for LC species:

P p L p = 1. ( 11
)
The density of these LC species is generally much lower that that of the ground state atoms and ions. The latter, in general large density reservoirs, are apart from chemistry, also ruled by transport. These species are denoted by transport sensitive (TS) species. The buffer gas atoms in ground state are excluded, since they are assumed to be stationary in space and time.

The above shows that the dimensionless quantity ν t p /D p can be employed as a tool to distinguish between LC and TS species. For the last category the competition between transport and chemistry is important meaning that we have to solve the corresponding transport equations while for the first that is not needed and the continuity equation can be simplified. This ratio can be determined by running the grand model and to find ν t p /D p (or P p /L p ) by post processing. Before doing so, we will perform some estimative calculations. We distinguish the following species:

• The buffer gas particles, the ground state atoms of He and Ar are assumed to be constant in time and space so they will not be equipped with a particle balance. • For excited neutral species we can assume that the transport is purely diffusive and given by ν t p = D p /R * 2 , where R * is in the order of the radius of the discharge. For the diffusion coefficient D p we use the expression D p = k B T g /(M p ν m ) with ν m frequency of momentum transfer from the species to the buffer gas atoms, in this case He. We can use ν m = n (He) v σ, where v = (k B T g /M (He) ) 1/2 is the thermal velocity of the He atoms; this is justified since the relative velocity is mostly determined by thermal velocity of the lightest particle (He). That means that the diffusion coefficient reads:

D p = (k B T g ) 3/2 M (He) M * p P σm p = 0.4 M * p m 2 s -1 , (12)
where M * p is the mass number of the atom, m p the proton mass and σ the cross section for momentum transfer. Inserting T g = 1000 K , P = 2.3 kPa and σ = 10 -19 m 2 , we get the value given at the right hand side. Of course the σ-value depends on the couple of interacting species but to get insight in the order of magnitude we took σ = 10 -19 m 2 . Inserting for R = 2 mm we find for the Cu and Ar atoms values in the order of ν t p = 2.10 3 s -1 . For excited He atoms this is more or less 40 times larger. For the excited atomic species we can use for the destruction frequency D p = 10 7 s -1 , which is taken equal to a typical value of the radiative decay frequency. So for excited species we get ν t p /D p values in the order of 10 -3 to 10 -2 , meaning that they can be considered as being determined by local chemistry.

• For the excited ions we only have to consider Cu + * , which will represent the upper laser level.

Apart from diffusion, this species will also be transported by drift. To get an estimate of the combination of drift and diffusion we can assume that the net effect leads to ambipolar diffusion. This implies a diffusion enhancement of the form D a = D p (1 + T e /T h ), meaning that the transport frequency will be about 50 times higher. Inserting the radiative decay frequency in order of 10 8 s -1 we find that ν t p /D p is in the order of 10 -3 . So that also the Cu + * species are determined by local chemistry.

• For the atomic and molecular ions we have to compare the ambipolar diffusion with recombination processes. Several recombination channels have to be considered, which can be classified in 2-particle or 3-particle recombination channels. Due to the (global) charge neutrality the destruction of ions is closely related to that of electrons and as the plasma is strongly ionising we can expect that electrons are TS. So the same must apply to the collection of ions. However, to understand the role of the various different ions we have to consult the model results in order to determine the LC ions.

Before to run the model some considerations can be made on the transition frequencies and the nature of the underlying processes. For the transition frequency related to the conversion of species p into q the transition frequency D p,q was introduced. In the case of radiative decay D p,l = A p,l , being the probability of the radiative decay of p to a lower level l. In the case of that 2 particles are involved we have D p,q = n q k (2) p,q where n q is the density of the particles colliding with p. For 3-particles interaction we have D = n x n y k (3) p,q . A further classification can be made on the role of the excitation agent, the particle of type x and y as given above the expressions of the frequencies. We start with the electrons. These are found to be of main importance, especially there, where the active zone plasma is created. These endothermic processes, including excitation and ionization, are denoted by electron excitation kinetics (EEK). Once the radicals (the excited particles, ions) are formed, they can interchange there internal energy by means of charge or excitation transfer. The collection of these processes is denoted by heavy particle excitation kinetics (HEK). The excess of internal energy will be used to heat the gas. If the internal energy is transferred to the electrons we talk about MEK: mixed excitation kinetics. An example of a MEK process is Penning ionization. Finally we have the exothermal processes, the collection of recombination and deexcitation processes.

Species and reactions included in the model

The buffer gas atoms are uniformly distributed in time and space, i.e. the gas temperature, the gas pressure and density are independent on the spatial position. The gas temperature is assumed to be 1000 K .

Table 1 lists the set of species for which the balance equations (equations ( 1) and ( 3)) were solved, together with the transport coefficients used in the model and the corresponding references.

Species p µ p × p (Torr m 2 V -1 s -1 ) D p × p (Torr m 2 s -1 ) Ref. e f 1 (ε) e q u a t i o n ( 1 3 ) [ 3 ] Ar + f 2 (E/N ) e q u a t i o n ( 1 3 ) [ 4 ] He + f 3 (E/N ) e q u a t i o n ( 1 3 ) [ 4 ] Cu + f 4 (E/N ) e q u a t i o n ( 1 3 ) [ 5 ] Cu + * f 5 (E/N ) e q u a t i o n ( 1 3 ) [ 5 ] Ar + 2 f 6 (E/N ) e q u a t i o n ( 1 3 ) [ 4 ] He + 2 f 7 (E/N ) e q u a t i o n ( 1 3 ) [ 4 ] Cu - 13.45 [6] Ar * - 20 [7] He * - 15.35 [7]
Table 1. The list of species for which the balance equation is solved, including the used transport coefficients and the corresponding references. The mobility coefficient for the electrons is specified as a function of the mean electron energy f (ε). For the ionic species it is given as a function of the reduced electric field f (E/N). The diffusion coefficients are deduced from the mobility using the Einstein relation (13).

The Cu + * in table 1 represents the excited ionic upper laser level, it is situated 24.5 eV above the ground state of atomic Cu.

The molecular ions are included as their influence could be of importance at the conditions under study. The intermediate states, the excited molecules, are not included in the model.

We assume that for the charged particles, the Einstein relation can be used to link the diffusion coefficients to the mobility:

D p = k B T p µ p q p , (13)
where q p is the elementary charge, and T p the particle temperature, corresponding to the energy of the random particle motion.

For the ions the local field approximation is used. This assumes a direct relation between the particle energy distribution and the electric field, hence the transport coefficients are regarded as being functions of the reduced electric field. These functions can be found in literature as a result of experiments and classical theories [START_REF] Ellis | At Data and[END_REF][START_REF] Mcdaniel | Collision phenomena in ionized gases[END_REF]. The mobility of He + and Ar + ions in their pure parent gases as a function of the reduced electric field are adopted from [START_REF] Ellis | At Data and[END_REF]. From this the mobilities in a He-Ar gas mixture are calculated using Blanc's law [START_REF] Blanc | [END_REF].

For electrons, however, substantial deviations from the local field approximation can be expected for typical HCD conditions. Due to the small mass as compared to that of the heavy particles, electrons created in a high E-field region can easily be launched to regions where the E-field is small while keeping (part of) the initially gained high energy. Therefore, rather than using a dependence of the electron properties on (E/N ), we have to solve the electron energy balance. This gives the mean electron energy ε(x) as a function of position. Subsequently the electron transport coefficients can be computed using the local f (ε) values. The data are obtained from the free-ware Boltzmann equation solver BOLSIG+ [3], which apart from the transport and reaction rate coeffcients gives insight in the electron energy disctribution function as well.

Since the individual metastable helium states participate in similar reactions with very similar rate coefficients [9], they are combined into one effective level, lying at 20.215 eV above the ground level. The same applies to the Ar metastable levels: the metastable levels are combined into one effective level lying at 11.55 eV above the argon ground state. Other excited states are not included in the model. In section 4.3 we will investigate what happens to the main plasma properties when the total excitation to all the excited levels is being set equal to ionization. By doing so, we in fact involve all the excited levels as stages in the ladder-climbing ionization process. This can be seen as giving the maximum in effective ionization. Excited states of sputtered Cu atoms are not taken into account since we do not expect that the (de)excitation of these levels will affect the electron energy and particle balance substantially.

Table 2 gives the complete set of reactions together with the reaction rate coefficients used in the model: the first 7 lines give the reactions induced by EEK, the group 8 -11 are HEK, the group 12-18 are MEK. The next group of reactions from 19 to 22 are the recombination processes followed by the radiative process 23.

As stated before, the buffer gas atoms, He and Ar in ground state, are assumed to be uniformly distributed in the discharge whereas the ground state copper atoms are produced by sputtering only. The atoms in ground state are ionized by electron collisions: direct ionization (reactions 3, 4 and 7) and excited to the lumped levels Ar * and He * (reactions 1 and 5). These levels can be converted into ions by means of electron collisions (reactions 2 and 6) and Penning ionization (reactions 12, 14, 15, 17 and 18). The HEK includes charge transfer reactions between the buffer gas ions and metal atoms in ground state (reactions 8 and 9). The processes of molecular ion formation include associative ionization (reactions 13 and 16) from the metastable levels and ion conversion (reactions 10 and 11), while the destruction process is dissociative recombination (reactions 20 and 21). The density of the excited Cu ionic level is mainly generated by charge transfer of He ions to Cu atoms (reaction 9) and decay spontaneously to the ground ionic level of Cu (reaction 23).

Results and discussion

The calculation results include the spatial distribution of the densities and fluxes of the species, as well as the rates of their production and loss processes. These are used to get volume averaged values of these quantities. the table it can be seen that the rates of excitation and ionization of Ar are much larger than those of He. This is because the ionization (excitation) potential of Ar is lower (24.58 versus 15.76 eV for ionization and 20.215 versus 11.62 eV for excitation). This implies that the Ar ion is the main ionic species in the discharge in spite of the fact that Ar consists of only 5% of the gas mixture. Comparing the electron excitation kinetics EEK with HEK shows that the electron impact processes have the highest rates. This makes that the system can be seen as an ionising EEK plasma. • The rates of the backward processes, atomic recombination (reactions 19 and 21), are in the order of 10 16 m -3 s -1 for He + and Ar + . Since they are 8 orders of magnitude lower than the forward process, it is obvious that they can be neglected.

Chemistry analysis

• The excited ion level Cu + * is only produced by charge transfer with He atoms (reaction 9) and decay spontaneously to Cu + (reaction 23). It can be seen from table 3 that the rates of these two reactions are the same, meaning that the criteria (11) holds for Cu + * . This confirms what was found before: Cu + * is a LC species. • The production processes of molecular ions include ion conversion (reactions 10 and 11) and associative ionization (reactions 13 and 16). The calculated density of He + 2 is less than 1000 smaller than the density of He + . The same holds more or less for the ratio Ar + 2 /Ar + . For Ar + 2 the dominant production process in the associative ionization with a rate in the order of 10 23 m -3 s -1 whereas the ion conversion rate is in order of 10 19 m -3 s -1 . Due to the low densities of He + 2 and Ar + 2 and consequently low fluxes to the cathode wall, the contribution of the molecular ions to sputtering can be neglected.

Nr. Reaction

Rate (m -3 s -1 ) Table 4 presents the calculated contribution in percents of every reaction to the production/destruction rate for each relevant species. The ratio between the production and destruction rate P p /L p is shown as well. This helps to determine the locality/non-locality of the species.

1
• Electrons. The most important electron production processes are the direct (∼ 20%), and the stepwise ionization (∼ 60%) of Ar. Ionization of Cu contributes with about 13%. This is a substantial contribution especially in view of the fact that the Cu atom density forms less than 0.1% of the gas mixture. The reason lies again in the ionization potential; this is lower than that of Ar and He. The Penning processes contribute with a only a few percents to the creation of electrons.

From table 4 can be seen that the loss rate of electrons is two orders of magnitude lower than the production rate, so that P p /L p 1, As it was expected the electrons are TS species. • Excited species. The Ar excited states are produced mainly (98.7%) by electron impact excitation of the ground state and are predominantly lost by ionization (89.1%). Only a few percents is lost by MEK processes (reactions 12, 13 and 14). For He * the production is 100% due to electron impact excitation of the ground level. The Penning process that transforms Ar ground atoms into Ar + (reaction 17) appears to be the dominant loss process of He * (58.9%); another substantial destruction channel is that of ionization (39%).

From table 4 it can be seen that the excited gas species are completely determined by the reactions occurring in the discharge: P/L = 1, which completely agrees with the considerations given in section 2. However, despite of the locality, they give an important contribution to the (stepwise) ionization. Around 80% of the He ions are produced by stepwise ionization versus 20% by direct ionization. For Ar + the ratio is more or less the same. As 4. Calculated contribution in percents of every reaction to the production/destruction rate for every species presented.

discussed in section 2, for LC species it is not necessary to solve the transport equation ( 3). This speed up the calculations. Concluding we may state that there is no need to employ the particle balance in full glory for the computation of the density of excited gas species Ar * and He * . As LC species local production/destruction balances suffice. However, the species can not be removed since they serve as important intermediate stages in the ionization processes. • Molecular ions. For He + 2 the production is mainly (∼ 74%) due to ion conversion process and associative ionization (∼ 26%). They are lost by dissociative recombination. The calculated He + 2 density is in the order of 10 14 m -3 . From table 4 it can be seen that these processes give minor contributions for the production/destruction of the other species. The He + 2 are unprofitable in the discharge. For Ar + 2 the main production process (99.9%) is associative ionization (reaction 20). From table 4 it can be seen that this process have minor effect to the production/destruction of other species. The contribution of the ion conversion process to the production of Ar + 2 is negligible (0.02%); moreover this process does not contribute to the production/destruction of any other species, hence it can be neglected. The dissociative recombination of Ar + 2 appears to be the main loss process of electrons. However, the calculated rate for this process is two orders of magnitude lower than the total ionization. Excluding this process will not affect the electron density because the ionization processes are the dominant processes in the discharge. The ratio P p /L p of He + 2 is ∼ 18. That means the He + 2 is almost transport driven. This is not so surprising since He + 2 has a high mobility. The ratio between the production and destruction processes for Ar + 2 is 2 and indicates that the density of Ar + 2 is predominantly determined by the local reactions in the discharge. At the condition under study, the locality of the Ar + 2 allows even to ignore the presence of the Ar molecular ions; the density is small and the contribution to production or destruction for other species is negligible. The elimination of the molecular ions is discussed in next subsection.

Molecular ions

To analyse the possible consequences of ignoring molecular ions and the related reactions, two models were constructed: the first one is equipped with the complete set of species and reactions as shown in the tables 1 and 2; the second model is a simplified model with reduced chemistry according to the observations above, i.e. excluding molecular ions and the relevant reactions, and atomic recombination processes. For both models the power is set to 300 W while the pressure is chosen to be 2.3 kPa .

Figure 1 compares the electron, He + and Ar + densities obtained by the two models. It is clear that the presence of molecular ions does not affect the density distribution of other species behaviour in the discharge. They can be excluded in the reduced chemistry model.

Ladder climbing

In section 2 was shown, and in subsection 4.1 confirmed by the model, that the metastable levels are LC species. They are created predominantly by excitation and immediately lost by ionisation, contributing greatly to the ionization degree. However, in practice EEK processes to higher excited levels can also contribute to the ionization degree; the so-called ladder-climbing processes might be of importance [14]. In order to check the importance/unimportance of these processes, we will construct another model and again compare the results with the complete model.

From the same considerations as described above, we can expect that species in all the possible excited states are LC species and that they, after being created, are immediately ionized. So that we can consider that the total excitation rate equals to the total ionization rate. With this assumption, the reduced chemistry model can be further simplified excluding completely the metastable levels and hence omitting the intermediate step of excitation. So, the reactions left in the reduced chemistry model are presented in table 5. The EEK rate coefficients as a function of Nr. Reaction Rate coefficient, k r (m 3 s -1 ) References the mean electron energy are replaced with the rate coefficient for the total excitation. From the HEK processes we have left only the charge transfer processes of metal atoms with gas ions. Table 6 presents the densities of the active species, averaged over the volume in comparison with the complete model. Table 6 shows small differences in the averaged values of the densities. The densities are slightly higher for the simple model. The densities of electrons and Ar ions are higher for the simplified model, while the density of He ions is lower. The reason is that the increased ionization in the simplified model results in lower electron energy. The ionization rate will be higher for species with lower ionization potential. For Cu ions the difference is more pronounced also because the increased Ar ion density results in increased sputtering, hence the density of Cu atoms in the discharge. Nevertheless, there is not considerable change in the species densities.

Figure 2 presents the axial profiles of the electron density and the ion densities. It can be seen that the axial profiles of the main charged particles remains more or less the same. The difference lies in the regions where the plasma density is highest. Apart from the slightly changes in the maximum values of the densities, the spatial density distribution is not changed significantly. We have to conclude that the contribution to the ionization degree due to ladder-climbing is negligible at the conditions under study.

Conclusions

In a search of a reduced chemistry module for the description of the plasma behaviour in a HCD with a He-Ar-Cu mixture, estimative calculations and numerical simulations are performed. This reduced chemistry model aims to construct a lean and reliable model that can be used as part of a design tool of HCD lasers.

Analysing the various species and their behaviour we determined the species that are not essential for the discharge, meaning that the presence of these species does not affect the main plasma properties (spatial values of the electron density and mean energy) so that they are not essential for the plasma application.

Based on the estimative calculations, numerical simulations and the post processing of the modelling results, we can summarise the following:

• The HCD plasma is characterised as an ionising electron excitation kinetics (EEK) plasma;

the main ionic species is Ar + , despite the fact that Ar constitute only 5% of the gas mixture. • Being an ionising plasma, the atomic recombination processes can be neglected.

• Electrons and ions are transport sensitive (TS) species, while excited species (atom and ion) are local chemistry (LC) species. This observation results in simplification of the continuity equations for the LC species as the transport term is zero. • The influence of the molecular ions is negligible at the conditions under study. Although in many cases the molecular ions could appear as an important recombination chanel, it was shown that for the conditions under study all the recombination processes can be neglected with respect to the ionization processes. • The contribution to the ionization degree due to ladder-climbing is negligible at the conditions under study.

Taking the statements above into considerations, enables to construct a lean and reliable model, without affecting the main plasma properties and without loss of accuracy. With such a chemical lean model it is than possible to find the best of the geometrical construction, the anode cathode patterns, the current settings, the fill-chemistry, etc. The technique developed in this study can be applied to glow discharges in general and to ionising electron excitation kinetics (EEK) plasmas.

Figure 1 .

 1 Figure 1. Comparison of the axial density profiles of two models with and without molecular ions.

Figure 2 .

 2 Figure 2. Comparison of the axial density profiles of two models: the complete model and the simpler one (without excited states).

Table 3

 3 presents the reaction rates of each reaction averaged over the volume. From this table the following information can be deduced.

	Nr. Reaction	Rate coefficient, k r	References
	1 e +Ar → Ar * + e	k 1 (ε) m 3 s -1	[3]
	2 e +Ar * → Ar + + 2e	k 2 (ε) m 3 s -1	[3]
	3 e +Ar → Ar + + 2e	k 3 (ε) m 3 s -1	[3]
	4 e +Cu → Cu + + 2e	k 4 (ε) m 3 s -1	[3]
	5 e +He → He * + e	k 5 (ε) m 3 s -1	[3]
	6 e +He * → He + + 2e	k 6 (ε) m 3 s -1	[3]
	7 e +He → He + + 2e	k 7 (ε) m 3 s -1	[3]
	8 Ar + + Cu → Ar + Cu +	3.16 × 10 -16 m 3 s -1	[10]
	9 He + + Cu → He + Cu + *	1.0 × 10 -15 m 3 s -1	[10]
	10 Ar + + 2Ar → Ar + 2 + Ar 11 He + + 2He → He + 2 + He 12 Ar * + Ar * → Ar + + Ar + e	9.66 × 10 -56 m 3 s -1 6.8 × 10 -56 m 3 s -1 1.17 × 10 -15 m 3 s -1	[11] [12] [11]
	13 Ar * + Ar * → Ar + 2 + e 14 Ar * + Cu → Ar + Cu + + e	2.03 × 10 -15 m 3 s -1 4.4 × 10 -16 m 3 s -1	[11] [10]
	15 He [10]
	19 Ar + + 2e → Ar + e	k 8 (ε) m 3 s -1	[3]
	20 Ar + 2 + e → Ar * + Ar 21 He + 2 + e → He * + He 22 He + + 2e → He + e	k 9 (ε) m 3 s -1 k 10 (ε) m 3 s -1 k 11 (ε) m 3 s -1	[11] [12] [3]
	23 Cu + * → Cu + + hν	0.23 × 10 9 s -1	[13]

• The buffer gas atoms (Ar and He) are ionized mainly by electron impact; this can be due to direct ionization or stepwise ionization, that is ionization intermediated by excitation. From * + He * → He + + He + e 0.87 × 10 -15 m 3 s -1 [12] 16 He * + He * → He + 2 + e 1.5 × 10 -15 m 3 s -1 [12] 17 He * + Ar → He + Ar + + e 1.68 × 10 -16 m 3 s -1 [10] 18 He * + Cu → He + Cu + + e 9.48 × 10 -16 m 3 s -1

Table 2 .

 2 Reaction

rate coefficients used in the model. The electron impact reactions are specified as a function of the mean electron energy kr(ε).

Table 3 .

 3 Ar + + e + Ar 1.3 × 10 23 13 Ar * + Ar * → Ar + 2 + e 2.2 × 10 23 14 Ar * + Cu → e + Ar + Cu + 1.32 × 10 23 15 He * + He * → e + He + He + 6.73 × 10 19 16 He * + He * → He + 2 + e 1.16 × 10 20 17 He * + Ar → He + Ar + + e 2.61 × 10 23 18 He * + Cu → e + He + Cu + 8.59 × 10 21 19 Ar + + e + e → Ar + e 1.34 × 10 16 Calculated reaction rates averaged over the volume.

	e+Ar → Ar * + e	7.75 × 10 24
	2 e+Ar * → Ar + + 2e	6.77 × 10 24
	3 e+Ar → Ar + + 2e	2.16 × 10 24
	4 e+Cu → Cu + + 2e	1.42 × 10 24
	5 e+He → He * + e	4.46 × 10 23
	6 e+He * → He + + 2e	1.73 × 10 23
	7 e+He → He + + 2e	3.71 × 10 22
	8 Ar + + Cu → Ar + Cu +	4.86 × 10 22
	9 He + + Cu → He + Cu + *	3.44 × 10 21
	10 Ar + + 2Ar → Ar + 2 + Ar 11 He + + 2He → He + 2 + He 12 Ar 20 Ar + 2 + e → Ar * + Ar 21 He + + e + e → He + e	4.72 × 10 19 3.35 × 10 20 1.04 × 10 23 6.04 × 10 16
	22 He + 2 + e → He * + He 23 Cu + * → Cu + + hν	2.56 × 10 19 3.2 × 10 21

* + Ar * →

Table 5 .

 5 Reaction rate coefficients used in the simple model.

Table 6 .

 6 Species densities averaged over the volume. Comparison between the complete model and the simple one.

	Density, m -3 Complete Model Simple Model
	e	7 .85 × 10 18	9.14 × 10 18
	Ar +	7.29 × 10 18	8.81 × 10 18
	He +	2.03 × 10 17	1.76 × 10 17
	Cu +	1.68 × 10 17	2.48 × 10 17
	Cu	3.58 × 10 19	4.52 × 10 19

Acknowledgments

This work was done as part of "Physical chemistry of plasma-surface interaction" (PSI) in the framework of the Belgian federal programme "Interuniversity Attraction Poles" (IAP).

The authors acknowledge the support of the Dutch National Programme BSIK, in the ICT project BRICKS, theme MSV1 and the support of the National Science Fund of Bulgaria, project DO 02-274/2008.