J Gorin

- M Wipliez

- J Piat

-F Prêteux

- M Raulet

AN LLVM-BASED DECODER FOR MPEG RECONFIGURABLE VIDEO CODING

Keywords: Reconfigurable Video Coding, RVC-CAL Actor Language, MPEG decoder, Low Level Virtual Machine, Dataflow programming, Multi-core, Code synthesis

. RVC-CAL naturally expresses potential parallelism between tasks of an application, which makes an ADM description suitable for implementation to a wide variety of platform, from uniprocessor systems to FPGAs. MPEG RVC eases the conception process of decoders by describing decoders at a library component level instead of using monilithic algorithms, and by providing a library of coding tools standardized in MPEG. This paper presents new mechanisms based on the Low Level Virtual Machine (LLVM) capacities that allow the conception of the first decoder able to dynamically instantiate an RVC decoder description. This decoder, unlike static decoders generated by RVC tools [2], keeps de facto the features of an RVC description namely portability, scalability and reconfiguration ability.

INTRODUCTION

MPEG multimedia coding technology has delivered many heterogeneous coding standards. The specification of such standards has been done case-by-case providing monolithic textual description and reference software in C++. Very little attention has been given to provide a formalism that would explicitly present the common components of different standards and that would furthermore be suited to the heterogeneous panel of systems available nowadays. MPEG structured their standards with many possibilities of algorithm combination called Profiles. Selecting an appropriate profile for a selected platform would enable a codec designer to have any desired trade-off between compression performance and implementation complexity. Currently, interoperability demands that the selection process for a profile be described into the normative description of a codec, or at best, into a number of choices codified within the media syntax.

MPEG Reconfigurable Video Coding (RVC) has been chosen by the MPEG community to be an alternative paradigm for codec deployment. The MPEG RVC paradigm is based on RVC-CAL Actor Language (RVC-CAL) to describe decoders at high-level library component using dataflow descriptions. The main objective of RVC is to enable arbitrary combinations of fundamental algorithms, without additional standardization steps. By adding the side-information of the combination description alongside the content itself, MPEG RVC defines the new concept of RVC decoder. An RVC decoder may create, configure and re-configure video compression algorithms adaptively to its content.

Yet, no mechanism has been found to automatically and dynamically use dataflow description to form an RVC Decoder. Our work presented in this paper proposes to transform the RVC-CAL description of coding tools into the generic low-level description called Low-Level Virtual Machine (LLVM) Intermediate Representation (IR), and to use the LLVM infrastructure for dynamically and efficiently instantiating these coding tools to create decoders. By combining the LLVM and the RVC concepts, we created a portable and universal MPEG decoder engine that can configure and reconfigure an MPEG RVC decoder description. This decoder has been successfully tested onto multiple platforms.

MPEG RECONFIGURABLE VIDEO CODING

Since the year 2004, MPEG has become very active about video compression/decompression application prototyping coming from their coding standards. These works led to the creation of the MPEG Reconfigurable Video Coding framework. This framework aims at "allowing a dynamic development, implementation and adoption of standardized video coding solutions with features of higher flexibility and reusability" [START_REF] Bhattacharyya | Overview of the MPEG reconfigurable video coding framework[END_REF]. Its key approach is to provide an Abstract Decoder Model (ADM) of existing or new MPEG standards at system-level suited for any platform.

An Abstract Decoder Model, shown in Figure 1, is a generic representation of a decoder, built as a block diagram expressed with the XML Dataflow Format (XDF) [START_REF]Information Technology -MPEG systems technologies -Part 4: Codec Configuration Representation[END_REF]. XDF is an XML dialect that describes the connections between

X ML D a t a o w F o r ma t

Fig. 1. The reconfigurable Video Coding Framework. blocks called Functional Units (FUs). Each FU defines processing entities of a decoder and connections represent data flow between FUs. MPEG RVC is under development as part of the MPEG-B standard [START_REF]Information Technology -MPEG systems technologies -Part 4: Codec Configuration Representation[END_REF], which defines the framework and the language used to describe components; and as part of the MPEG-C [START_REF]Information technology -MPEG video technologies -Part 4: Video Tool Library[END_REF] standard, which defines the library of video coding tools (Video Tools Library or VTL) employed in existing MPEG standards.

MPEG RVC provides both a normative standard library of FUs and a set of decoder descriptions expressed as networks of FUs. An ADM representation of a decoder is modular and helps its reconfiguration by allowing the topology of its network to be easily modified. RVC mainly focuses on reusability by allowing different decoder descriptions to instantiate common FUs across standards.

RVC-CAL Dataflow Programming

FUs of an Abstract Decoder Model are defined using RVC-CAL, a subset of CAL Actor Language. RVC-CAL [START_REF] Eker | CAL Language Report[END_REF] is a textual and domain specific language for writing dataflow models, more precisely for defining Functional Units (or actors) of a decoder at a high level of description. An actor represents an autonomous entity, thus a composition of actors explicitly describes the concurrency of an application. The RVC-CAL Actor Language has been defined to be platform independent and retargetable to a rich variety of platforms. RVC-CAL, compared with CAL, restricts the data types, and operators that cannot be easily implemented onto the platforms.

An RVC-CAL actor is a computational entity with input ports, output ports, states and parameters. An actor communicates with other actors by sending and receiving tokens (atomic pieces of data) through its ports. An actor can contain several actions. An action defines a computation, which consumes sequences of tokens from input ports and produces sequences of tokens to output ports. Actions have data-dependent conditions for their execution. The execution of an action may change the actor internal state, so that the produced output sequences are functions of the consumed input sequences and of the current actor state.

RVC Decoder features

The main benefit of the MPEG RVC approach is to be able to describe a decoder without carrying implementation details. By using an RVC-CAL description, an Abstract Decoder Model has two benefits:

1. Parallelism scalability: While scalability of parallelism composes the principal weakness of traditional imperative languages, RVC-CAL proposes to encapsulate tasks into actors, explicitly exposing parallelism between tasks of an application.

Modularity:

The "untimedness" and the strong encapsulation of actors offer high degree of modularity. This property allows each actor of a dataflow model to be unbound to its environment and thus to be easily used in others.

C and HDL synthesis tools [START_REF] Bhattacharyya | Overview of the MPEG reconfigurable video coding framework[END_REF] can be used to automatically generate static decoders for specific platforms. These decoders may only take the useful information from an ADM description to fully exploit processing resources of the targeted platform. Our approach differs in the way that we skip this synthesis process and dynamically run an ADM description on the targeted platform. To be fully RVC compliant, this decoder must integrate a Video Tools Library, a library that supports RVC ADM representation and a Virtual Machine able to produce efficient Just-In-Time (JIT) compilation. By combining all these tools, video decoders (Fig. 2) can be created, configured and reconfigured adaptively to decode any video sequence or syntax.

LOW LEVEL VIRTUAL MACHINE (LLVM)

Performance and portability are crucial to develop a sustainable RVC decoder. High Level Language Virtual Machines (the most popular are Java Virtual Machine or Common Language Runtime) have generally high portability but poor performance compared to an equivalent C application [START_REF] Singer | JVM versus CLR: a comparative study[END_REF][START_REF] Lattner | LLVM: A Compilation Framework for Lifelong Program Analysis & Transformation[END_REF]. The Universal Video Decoder (UVD) [START_REF] Richardson | Dynamic Configuration: Beyond Video Coding Standards[END_REF], dedicated to video decoding, shows interesting performances but at the cost of developing a dedicated Virtual Machine, currently tested on a single environment. The Low-Level Virtual Machine fits all of our expectation by providing excellent application performance, a compiler infrastructure tested in a wide variety of platforms and a strong research infrastructure support.

LLVM Intermediate Representation

The centerpiece of LLVM is the LLVM Intermediate Representation (IR) using LLVM virtual instruction set. The LLVM instruction set is a very simple representation and language independent type-system that captures the key operations of ordinary processors but avoids machine specific constraints such as physical registers, pipelines, low-level calling conventions, or traps. The generic instruction set of LLVM constitutes an excellent low-level representation for FUs, allowing their representation to be directly executed into a wide variety of platforms. LLVM IR includes explicit type information, control flow graphs, dataflow representation along with a three-address code (3AC) and Static Single Assignment (SSA) form. These properties simplify transformations and code analyses to allow aggressive multistage optimization and high-performance execution onto its integrated Virtual Machine [START_REF] Lattner | LLVM: A Compilation Framework for Lifelong Program Analysis & Transformation[END_REF] .

LLVM compilation framework

LLVM also designates a compilation framework that exploits the LLVM IR to provide a combination of features not available in any previous compilation approach [START_REF] Lattner | LLVM: A Compilation Framework for Lifelong Program Analysis & Transformation[END_REF]. These capabilities are:

1. Persistent program information: The compilation model preserves the LLVM representation throughout an application's lifetime, allowing sophisticated optimizations to be performed at all stages of execution.

2. Transparent runtime model: The system does not specify any particular object model, exception semantics, or runtime environment, thus allowing any language to be compiled using it.

3. Uniform, whole-program compilation: Languageindependence makes it possible to optimize and compile all code comprising an application in a uniform manner.

This compilation framework corresponds to a collection of libraries and tools that makes easier to build offline compilers, optimizers or Just-In-Time (JIT) code generators. LLVM is currently supported on X86, X86-64, PowerPC 32/64, ARM, Thumb, IA-64, Alpha, SPARC, MIPS and CellSPU architectures. As LLVM is becoming a commercial grade research compiler, the code generated will continually benefit from improvements of its compiling infrastructure.

PORTABLE VIDEO TOOL LIBRARY GENERATION

The main purpose of this paper is to use the efficiency of the LLVM representation to provide a portable VTL manageable by the LLVM infrastructure. We describe in this part the translation process used to convert FUs described in RVC-CAL into an LLVM representation.

Functional Units transformation

The first constraint of the LLVM code generation is to avoid lost information from the original VTL, described in RVC-CAL. We used mechanisms presented in [START_REF] Wipliez | Software Code Generation for the RVC-CAL Language[END_REF], which describe the translation of an RVC ADM into a C representation for single processors. This C representation transformed FUs from VTL into several instances. As an instance is equivalent to FU but with resolved parameters, a direct translation of a C representation into LLVM would induce loss information from the VTL. In our approach, we extend the method presented in this previous paper by applying our transformation directly to the VTL and thus conserve modularity properties of FUs.

The first stage of our translation process, described in Figure 3, consists in parsing each Functional Unit from the VTL to an Abstract Syntax Tree (AST). This AST helps the application of a series of transformation and the conversion of the RVC-CAL into LLVM IR. The transformations applied to the AST are:

• Control Flow Graph (CFG) transformation: Actions are transformed in a set of basic blocks, and each basic block as a sequence of instructions, ending in exactly one terminator instruction.

• Static Single Assignment (SSA) and Three-Address Code (3AC) form: Each register is written in exactly one instruction, that takes one or two operands and produce a single result.The LLVM instruction set includes an explicit phi instruction, which corresponds directly to the standard (non-gated) φ function of SSA form [START_REF] Lattner | LLVM: A Compilation Framework for Lifelong Program Analysis & Transformation[END_REF].

• Strong type checking: Each variable is declared as integer type with an arbitrary width. This transformation checks and ensures the size coherence for each variable contained in an LLVM IR.

As presented in section 2.1, actions from an FU have datadependent conditions for their execution. We composed an actor with several functions that describe actions and an action scheduler. The action scheduler checks the presence and values of tokens on its input ports and executes actions that fit to their associated executing conditions. The rationale for using action scheduler is to conserve the encapsulation of an actor and to easily deport the execution of the global network to a scheduler inside the decoder of the targeted platform; we called it actor scheduler and detailed it on part 5.2.

LLVM code generator into the Open RVC-CAL Compiler framework

To ease the translation process of FUs, we integrate the LLVM actor code generation into the extensible Open RVC-CAL Compiler 1 (Orcc) Infrastructure. This compiling infrastructure, shown in Figure 4, has been structured to easily write code generators that targeting any language from a single Intermediate Representation. The Orcc specific Intermediate Representation preserves the properties of RVC-CAL representation while being at a lower level of description, with simple arithmetic expression, imperative statements and SSA property. Back-ends are already available for generating VHDL, Java, C and C++ representations from an Orcc IR.

For the need of our portable VTL, we developed a new back-end that converts the Orcc IR of RVC-CAL Functional Units into an LLVM Representation. As the Orcc IR directly embeds simple arithmetic expressions and SSA form, the translation of an RVC-CAL FU into an LLVM representation is greatly simplified. The developed LLVM backend transforms the Orcc IR from each coding tools of the VTL into a set of LLVM files, representing an only VTL portable on any platform supported by the LLVM infrastructure.

MPEG RVC is based on the idea that most of the tools used in video coding come from MPEG Standards. As the 1 Orcc is available at: http://orcc.sourceforge.net LLVM representation of coding tools are generics and directly suited for a wide range of platforms, our approach allows decoders to extend the RVC concept by providing FUs outside the VTL. Thus, a decoder can be equally formed by coding tools standardized or not standardized in MPEG-C, for instance by coding tools directly included inside the bitstream to decode. This opportunity opens significant new opportunities in multimedia coding, especially in adaptative decoding [START_REF] Richardson | Dynamic Configuration: Beyond Video Coding Standards[END_REF].

RVC DECODER ENGINE

The second step of our approach is to produce a decoder that dynamically instantiates an RVC description of a decoder according to a network description and our portable VTL. To achieve this goal, we create an engine called RVC Decoder Engine, which manages the LLVM infrastructure for dynamically translating LLVM IR into optimized machine code. This RVC decoder engine also integrates execution rules to use the generated decoder.

Network instantiation

The instantiation of a network designates the initialization of actors, structures and fifos of an RVC description. The dynamic instantiation is made possible by coupling the Linker, Optimizer and Just-In-Time Compiler from the LLVM Infrastructure with an XDF parser and our RVC decoder engine. The RVC decoder, described on Figure 5, has the role to manage the instantiation of a network in a six steps process:

1. XDF parsing: XDF description is parsed into a graph that describes the whole network. This graph contains information about the list of FUs in the VTL, instances of an FU and connections in the network.

FUs selection:

The necessary FUs are taken from the portable VTL and stored in memory in the form of LLVM modules.

3. Linking: Functions of FUs are changed to their instance name to avoid ambiguous calls. All functions are then links into a single module.

Optimization:

The generated single module passes through aggressive optimizations, selected according to their efficiency for the targeted platform.

5.

Compilation: Functions of the single LLVM module representing actions and action schedulers are dynamically translated into machine code.

6. FIFO instantiation: FIFOs are instantiated and connected to each functions. Our FIFOs are unidirectional circular buffers that avoid the use of semaphore.

The generated decoder is finally connected to the source that contained the encoded video bitstream.

Network execution

Once the decoder is created, the RVC decoder engine executes the whole network. The network scheduler we wrote is a simple round-robin scheduler following the Dataflow Process Networks (DPN) [START_REF] Lee | Dataflow Process Networks[END_REF] model. A DPN is a model of computation (MoC) where a group of sequential processes (in our case the actors) are communicating through unbounded FIFO channels. DPN models must be dynamically scheduled, hence our actor scheduler endlessly calls the action scheduler of every actor contained in the network. Actors in the network are scheduled one after the other according to an arbitrary order, in our case the XDF Parsing order.

The strength of our scheduler consists in the preservation of the scalability of the original model. Indeed, all actors are still considered as independent entities, without any knowledge about the execution sequence of actions. Therefore, the execution of the network can be made by more than one round robin scheduler. Starting from this observation, a round robin scheduler can contain from one to all the actor of a network. If a platform contains multiple cores, a group of FUs could be mapped onto several round robin schedulers and each scheduler can be affected onto a separate core of the platform. This scheduler enhances parallelism and pipelining of each process for the whole application.

The strength of our model constitutes also its principal weakness if we compare the achievement of our decoder with an equivalent sequential code for a uniprocessor system. As the scheduler does not contain any information about the order to execute actions for each actor, every action has to be tested before determining if it can be executed. This scheduler involves an important overhead that can be reduced by finding static execution rules in the original dataflow network. We plan in future works to reduce this overhead by coupling our scheduler with analyzing tools for dataflow networks that would automatically detect sequential execution order of actions [START_REF] Gu | Exploring the concurrency of an MPEG RVC decoder based on dataflow program analysis[END_REF].

EXPERIMENTAL RESULTS

This section presents the experimental results led on our decoder. These experiments shows that our VTL is portable and compares the achievement of the RVC decoder with an equivalent static C and Java decoders onto several Operating Systems (OS). With this aim in mind, we developed our RVC decoder, described in Figure 3, in C++ using LLVM 2.62 . We also used our LLVM backend to generate a portable VTL from RVC-CAL FUs standardized in MPEG-C. The FUs currently available in MPEG-C are the coding tools from MPEG-4 Part-2 Simple Profile (SP) and MPEG-4 Advanced Video Coding (AVC) standards. We compiled our developed RVC decoder and copied our generated portable VTL on several OS with an Intel E6600 Core2 Duo processor at 2.40 GHz running with Windows 7, Mac OS X 10.5 and Linux Ubuntu 9.10. Table 1 shows the number of FUs contained in the VTL and currently available in MPEG-C. Those two configurations of decoders described in [START_REF] Bhattacharyya | Overview of the MPEG reconfigurable video coding framework[END_REF] for the MPEG-4 Part-2 Simple Profile (SP) decoder and from [START_REF] Gorin | An RVC Dataflow Description of the AVC Constrained Baseline Profile Decoder[END_REF] for the MPEG-4 Advanced Video Coding(AVC) Constrained Baseline Profile (CBP) decoder are the most representative as they cover all the VTL. Some of these FUs are instantiated several times in decoders, the RVC description of the MPEG-4 SP decoder contains 64 instances and the RVC description of the MPEG- The same configuration of these two decoder has also been generated by the static C and Java synthesis tools included in RVC framework. The comparison results, showed in Table 2 andTable 3, compare the achievement of our RVC decoder with these two static implementation. These decoders were respectively tested on conformance testing sequences for SP decoders 3 and AVC decoders 4 .

FUs

A comparison of our decoder implementation with the equivalent static C decoders (i.e. without any Virtual Machine) shows that the impact of the LLVM Virtual Machine is unseen on Windows and Mac (OS) and has minor impact (roughly 20%) on Linux OS. On the contrary, our dynamic decoder is about 7 times faster than a static Java decoders running on the Java Virtual Machine (JVM). This speed factor can be explained by the fact that Java has no pointer mean. Each access to a FIFO in Java involves a memory copy of data, which puts pressure on the garbage collector of the Virtual Machine. Preliminary results show that the configuration and reconfiguration times of the MPEG-4 SP decoder are about 800 ms and about 1 second for the MPEG-4 AVC description. The reconfiguration times can be greatly improved by encapsulating dataflow network representation into bitstream and by supporting partial reconfiguration of decoders. We also tested the multi-core abilities of our decoder for a dual core processor. Two POSIX threads were used to implement two round-robin schedulers, with one round-robin scheduler per core. Each scheduler was precompiled with a list of actors manually distributed. The performance shows benefits of the multi-core (up to 1.5) depending on the configuration used. We have to find some mechanisms to have a smart and automatic dispatchment of the actors into several schedulers.

CONCLUSION AND PERSPECTIVES

The concept of such an RVC decoder implementation opens significant new opportunities, first in video decoding then in sound, 3D or any other medium that involve the purpose of a decoder. The main advantage of our approach is to couple the active research of LLVM and MPEG RVC. Its implementation, integrable into a wide variety of platforms, represents a good starting point for new research on adaptive decoding. The experimental results show the relevance of our approach by testing the portability, scalability and the fast configuration of two decoder samples.

However, this decoder is a base for many challenges. The DPN model of computation we use can be improved with dataflow analysis to be close to an equivalent sequential program. We plan to reduce the overhead induced by our scheduler by finding some mechanisms that could predict the next actions/actors to execute. The reconfiguration of a decoder involves yet a global change in the new decoder. We also plan to reduce reconfiguration times, by finding parts of a decoder that really needs to be changed. Finally, we prove that this decoder has scalable parallelism and rules should been implemented to automatically dispatch decoding algorithms onto the processing elements of a platform. The abilities brought by our modular and promising approach still require many new researches to produce real time High-Definition decoders.

Fig. 2 .

 2 Fig. 2. Representation of an RVC decoder.

Fig. 3 .

 3 Fig. 3. LLVM Code Generation for selected FUi.

Fig. 5 .

 5 Fig. 5. RVC decoder structure.

  Orcc framework with available backends.

	FUs FUs	front-end front-end Orcc	Intermediate Intermediate Representation Representation	LLVM back-end LLVM back-end C back-end C back-end Java back-end Java back-end
		Fig. 4.

Table 1 .

 1 Description of the generated portable VTL.

	MPEG-4 Simple Profile + MPEG-4 Advanced Video Coding	22 47
	Generated VTL	69

Table 2 .

 2 Decoder performance of an MPEG-4 Part-2 Simple Profile configuration for CIF sequences (352 × 288).

	tains 92 instances.	4 AVC con-
	C Windows (Visual Studio) 26,7 fps 3,5 fps 24,9 fps JAVA LLVM
	Linux (GCC)	39,3 fps 4,83 fps 24,6 fps
	MAC OS X (Xcode)	26,6 fps 4,85 fps 26,4 fps

Table 3 .

 3 Decoder performance of an MPEG-4 Advanced Video Coding configuration for QCIF sequences (176 × 144).

	C Windows (Visual Studio) 30,9 fps 2,8 fps 31,7 fps JAVA LLVM
	Linux (GCC)	48,5 fps 2,35 fps 33,5 fps
	MAC OS X (Xcode)	34,9 fps 2,78 fps 34,5 fps

LLVM 2.6 is available at: http://llvm.org/

Video sequences available at: http://standards.iso.org/

Video sequences available at: http://wftp3.itu.int/av-arch/jvt-site/


W Ettoumi

P Béjot

Y Petit

V Loriot

E Hertz

O Faucher

B Lavorel

J Kasparian
email: jerome.kasparian@unige.ch

J.-P Wolf

Spectral dependence of purely-Kerr

Keywords: numbers: 42.65.Jx Beam trapping, self focusing and defocusing, self-phase modulation, 42.65.Tg Optical solitons, 78.20.Ci Optical constants

come

The filamentation of high-power, ultrashort laser pulses is generally described as a dynamic balance between Kerr self-focusing and the defocusing by the plasma generated at the non-linear focus [1][2][3][4][5]. In this description, the Kerr-induced change in the refractive index is truncated to the first term n 2 I, where I is the local intensity. However, at higher intensities, the development has to be extended to higher-order terms in I, so that the real part of the refractive index at any frequency ω writes:

n(ω) = n 0 (ω) + ∆n Kerr (ω) = n 0 (ω) + j≥1 n 2j (ω)I j (1)
where the n 2j (ω) coefficients are related to the (2j+1) th order susceptibility tensor χ (2j+1) (ω), in the degenerate case where all considered fields are at frequency ω:

n 2j (ω) = (2j + 1)! 2 j+1 j!(j + 1)! 1 (n 2 0 (ω)ǫ 0 c) j ℜe χ (2j+1) (ω) (2)
In the last years, several numerical works have investigated the influence of the quintic nonlinear response on the filamentation dynamics at a wavelength of 800 nm, although without knowledge of its actual value [6][7][8][9][10]. They suggested that this term was defocusing, but considered it as marginal. Recently, the measurement of the higher-order Kerr indices at a wavelength of 800 nm up to n 8 in air and n 10 in argon [11] showed that they have alternate signs, and are therefore alternatively focusing and defocusing. Furthermore, by implementing these terms in a numerical simulation of filamentation, we have recently shown that the defocusing terms n 4 and n 8 , rather than the plasma, provide the main regularizing process in the filamentation of 30 fs pulses in air at 800 nm, so that plasma generation and propagation equations are almost decoupled [12]. This finding provided an explanation to measurements of plasma-free filamentation [13,14] and predicts symmetrical temporal pulse shapes, in contrast with a balance between the instantaneous Kerr term and the timeintegrated plasma contribution, which implies strongly asymmetric pulse shapes [15]. It also explained the discrepancy, by almost two orders of magnitude, between experimentally measured and numerically derived electron densities within filaments. While the experiments yield some 10 14 cm -3 [16,17], the numerical simulations require a few 10 16 cm -3 to balance the n 2 I Kerr self-focusing term [3,4]. The consideration of the higher-order Kerr terms also turned out to be necessary to obtain a quantitative agreement between numerical simulations and experimental results about the propagation of ultrashort infrared pulses in an argonfilled hollow-core fiber [18,19].

However, the ionization rates are higher at shorter wavelengths, so that ionization is generally believed to be much stronger in the case of ultraviolet filamentation [20], while its low efficiency in the infrared would expectedly prevent self-guiding of filaments. But the recently derived generalized Miller formulae [21] predict larger absolute values of the higherorder non-linear indices at shorter wavelengths, with faster spectral dependencies for the higher orders. As a consequence, the relative contribution to self-guiding cannot be easily extrapolated from qualitative discussions.

In this Letter, we numerically investigate these relative contributions from the nearultraviolet to the near-infrared. Using the values of the n 2j indices at any wavelength as obtained from the generalized Miller formulae [21], and the values recently measured at 800 nm [11], we simulate the filamentation of laser pulses from 300 nm to 1600 nm in air and argon. We show that filaments are efficiently generated at all wavelengths, even in the infrared. Moreover, the plasma marginally contributes to self-guiding in the filamentation of 30 fs laser pulses in argon for wavelengths longer than typically 400 nm. In air, where the ionization of oxygen is about 100 times more efficient than in argon, the Kerr terms still provide the largest defocusing contribution, although the plasma contribution can be neglected over the whole propagation length only in the infrared. This finding strongly impacts the plasma generation. We also find that ultraviolet wavelengths are not optimal to maximize ionization in a filament.

Numerical simulations are performed, as described in detail in [12], by solving a nonlinear Schrödinger equation taking the higher-order Kerr terms into account. The reduced scalar envelope ε defined such that |ε(r, z, t)| 2 = I(r, z, t), I being the intensity, is assumed to vary slowly in time and along z:

∂ z ε = i 2k △ ⊥ ε -i k ′′ 2 ∂ 2 t ε + 1 + i ω ∂ ∂t i k n 0 j≥1 n 2j |ε| 2j ε -i k 2n 2 0 ρ c ρε - ε 2 ℓ=O 2 ,N 2 σ ℓ (ω)ρ + W ℓ (|ε| 2 , ω)U ℓ |ε| 2 (ρ nt ℓ -ρ) (3)
where ω and k=n 0 ω/c are the angular frequency and wavenumber of the carrier wave, k ′′ accounts for the linear group-velocity dispersion, ρ is the electron density, ρ nt ℓ the density of neutral molecules of species ℓ, ρ c = m e ǫ 0 ω/q 2 e the critical plasma density and m e and q e the mass and charge of the electron, n 0 is the linear refractive index at λ, W ℓ (|ε| 2 ) is the photoionization rate of species ℓ with ionization potential U ℓ , σ ℓ is the cross-section for avalanche ionization as defined below in Equation ( 8) and t refers to the retarded time in the reference frame of the pulse. The right-hand terms of Eq.( 3) account for spatial diffraction, second order group-velocity dispersion (GVD), Kerr self-focusing (including the self-steepening term), defocusing by the higher-order nonlinear refractive indices, plasma defocusing, inverse Bremsstrahlung and multiphoton absorption respectively. We neglect the delayed orientational response, which for pulses longer than 100 fs would increase the self-focusing term [3,4] and affect the ionization efficiency of N 2 and O 2 molecules by less than 20 and 10%, respectively [22,23]. These opposite effects are negligible in the numerical simulations for 30 fs pulse duration, and do not affect qualitatively the discussion below even for longer pulses. We also neglect space-time focusing. However, in the following we mainly focus on the self-guiding process, peak intensity and ionization, which are little affected by this approximation.

The spectral dependence of the NLSE (3) stems from the plasma contribution as well as the dispersion of the linear (n 0 ) and non-linear (n 2j ) refractive indices. The latter can be deduced at any frequency ω from those of O 2 and N 2 at the same frequency by following the Lorenz-Lorentz relation, which links the refractive index of a mix of non-polar gases to its components [START_REF] Böttcher | Theory of Electric Polarisation[END_REF]:

n 2 mix (ω) -1 n 2 mix (ω) + 2 = ρ i n 2 i (ω) -1 n 2 i (ω) + 2 (4)
where n(ω) is defined in Equation ( 1) and ρ i denotes the relative abundance of the species i in the mix. Considering that ∆n Kerr ≪ 1, a first-order development of Equation ( 4) yields, for any order j:

n 2j,Air (ω) = 0.79 • n 2j,N 2 (ω) + 0.21 • n 2j,O 2 (ω) (5)
The values of the n 2j for argon, nitrogen and oxygen can be calculated at any frequency ω from their values measured at λ 0 =800 nm [11] and the dispersion curves in thoses gases [START_REF] Zhang | [END_REF], through the generalized Miller formula [21] expressed in term of non-linear refractive indices:

n 2j (ω) = n 2j (ω 0 ) n 2 0 (ω) -1 n 2 0 (ω 0 ) -1 2(j+1) (6)
While n 8,Air varies by a factor of 2 between 300 and 1600 nm, ionization displays an even much steeper spectral dependence. More specifically, the temporal evolution of the electron density is given by

∂ρ ∂t ≈ ℓ=O 2 ,N 2 W ℓ (I, ω)ρ 0,nt ℓ + σ ℓ (ω) U ℓ Iρ (7)
where ρ 0,nt ℓ is the initial density of neutral molecules of species ℓ. Here, attachment to neutral molecules and recombination with positive ions have been neglected owing to the short pulse durations considered in this work. The cross-section for avalanche ionization is calculated on the basis of Drude's theory [3]:

σ ℓ (ω) = q 2 e m e ǫ 0 n 0 (ω)c ν e,ℓ 1 + ω 2 ν 2 e,ℓ (8)
≈ q 2 e ν e,ℓ ω 2 m e ǫ 0 n 0 (ω)c (9) where ν e,ℓ is the mean collisional frequency of an electron with the species ℓ (i.e., the average electron velocity, divided by the mean free path of an electron, assuming that only species ℓ is present), and c is the speed of light. At atmospheric pressure in air, ν e,O 2 = 1/(1.75 ps), ν e,N 2 = 1/(440 fs), and ν e,Ar = 1/(350 fs). The multiphoton/tunnel ionization rates are given by the multi-species generalized Keldysh-Perelomov, Popov, Terent'ev (PPT) formulation [3,16]:

W ℓ (|ε| 2 , ω) = 4 √ 2 π C n * ℓ ,l * ℓ 2 4 √ 2U 3 2 ℓ E p 1 + γ 2 ℓ 2n * ℓ -3 2 -|m ℓ | × f (l ℓ , m ℓ ) |m ℓ |! e -2ν ℓ " sinh -1 (γ ℓ )- γ ℓ √ γ 2 ℓ +1 1+2γ 2 ℓ # U ℓ γ 2 ℓ 1 + γ 2 ℓ × +∞ κ ℓ ≥ν ℓ e -α ℓ (κ ℓ -ν ℓ ) Φ m β ℓ (κ ℓ -ν ℓ ) , (10)
where, expressed in atomic units,

E p = |ε| 2/(ǫ 0 c), γ ℓ = ω √ 2U ℓ /E p , ν ℓ = U ℓ (1 + 1/(2γ 2 )) /( ω), β ℓ = 2γ ℓ / 1 + γ 2 ℓ , α ℓ = 2 sinh -1 (γ ℓ ) -γ ℓ / 1 + γ 2 ℓ , and Φ m (x) = e -x 2 x 0 (x 2 -y 2 ) |m ℓ | e y 2 dy. n * ℓ = Z ℓ / √ 2U ℓ the effective quantum number, l * ℓ = n * ℓ -1
, l ℓ and m ℓ are the orbital momentum and the magnetic quantum number, respectively. In air, l ℓ = m ℓ = 0 [26]. Z ℓ is the residual ion charge accounting for the difference between the O 2 and N 2 molecules and their atomic counterparts. These empirical coefficients Z O 2 = 0.53 and Z N 2 = 0.9 have been measured at 800 nm [27], and are expected to be independent from wavelength. Since argon is an atomic gas, Z Ar = 1. The factors

|C n * ℓ ,l * ℓ | and f (l ℓ , m ℓ ) are |C n * ℓ ,l * ℓ | = 2 2n * ℓ n * ℓ Γ(n * ℓ + l * ℓ + 1)Γ(n * ℓ -l * ℓ ) , (11)
f (l ℓ , m ℓ ) = (2l ℓ + 1)(l ℓ + |m ℓ |)! 2 |m ℓ | |m ℓ |!(l ℓ -|m ℓ |)! . ( 12
)
To quantify the relative contributions of the higher-order Kerr terms (n 4 through n 10 )

and of the ionization to the defocusing which balances the self-focusing, we define the instantaneous ratio ξ between the refractive index changes induced by both of these contributions at any location r:

ξ( r, t) = | j≥2 n 2j I( r, t) j |/ ρ( r, t) 2n 0 ρ c ( 13
)
This expression is in fact the ratio of the magnitude of the two defocusing terms in the propagation equation ( 3), namely those accounting for higher-order Kerr terms and plasma defocusing, respectively. When considering the overall action of both effects on the whole pulse duration, we define a pulse-integrated value of ξ:

ξ( r) = | j≥2 n 2j I( r, t) j | • |ε( r, t)|dt/ ρ( r, t) 2n 0 ρ c |ε( r, t)|dt, (14)
We numerically integrated the propagation equation ( 3) for an ultrashort pulse typical of laboratory-scale filamentation experiments: 30 fs Fourier-limited FWHM pulse duration, a peak power of 6.5 critical powers P cr = λ 2 /4πn 2 , a beam diameter of σ r = 4 mm, a focal length f = 1 m and a pressure of 1 bar of either air or argon. The main results are displayed in Figure 1.

Our simulations yield filamentation over the whole investigated spectral range (300 -1600 nm), reproducing experimental observations from the UV [28,29] to the mid-IR [30]. As is visible in Figure 1 (a) and (b), the clamping intensity, filament onset and filament length are very similar in air and argon over the whole considered spectral length for a given incident reduced power P/P cr . Moreover, longer wavelengths yield longer filaments with an earlier onset. Furthermore, the output spectrum after 1.5 m propagation (panels (e) and (f)) is broader for longer wavelengths. As a result, the relative broadening, defined as the ratio of the output spectral width to the initial frequency, ∆ω/ω 0 , is almost constant across the spectrum. Spectral properties appear very similar in air and argon. In contrast, the electron density is approximately 10 times higher in the former than in the latter. The spectral dependence of the electron density is very non-monotonic (Panels (c) and (d)). On one hand, due to steps in the number of photons required for ionization, the electron density is not a monotonic function of the wavelength. For instance, ionization in air is almost 2 times more efficient at 793 nm than at 815 nm (See Figure 2). On the other hand, contrary to expectations that shorter wavelengths should result in stronger ionization, a maximum in the peak electron density is observed in the 610 nm range in the case of air, and around 470 nm in argon (Figures 1(c),(d) and 4(a)). Away from this maximum, the peak electron density decreases within a dynamics of typically one order of magnitude. This unexpected behavior stems from the convolution of the respective spectral dependences of (i) the ionization rate W , which increases at shorter wavelengths and (ii) the peak intensity, which decreases in the UV. This decrease is due to the fact that, according to Equation ( 6) and considering the typical dispersion curves in gases, the higher-order indices increase faster, in absolute values, when the frequency increases. As a consequence, the clamping intensity canceling the Kerr effect I ∆n Kerr =0 is lower, as shown on Figure 3.

The spectral dependence of the peak electron density by more than one order of magnitude, also evidenced on Figure 4(a), appears in contradiction with numerical results obtained without considering the higher-order Kerr terms [31], which predict almost similar electron densities, close to 10 16 cm -3 , at the three investigated wavelengths (248, 800 and 1550 nm).

Since the latter results were obtained with longer pulses (127 fs) of slightly lower power than in our work, a direct quantitative comparison cannot be performed. However, we expect that the qualitative difference between our results and those of Ref. [31] are due to the inclusion of the higher-order Kerr terms in our model, and thus illustrate the influence of the latter.

The very similar behavior, except for the plasma density, of two gases with comparable values of the non-linear refractive indices but significantly different ionization potentials, suggest that filamentation is driven by the higher-order Kerr terms rather than by plasma, not only at 800 nm as evidenced recently [12], but also on the whole investigated spectral range in both air and argon. Indeed, the on-axis ξ ratio (Figure 1(g),(h)) exceeds 1 in all considered conditions. Furthermore, the higher-order Kerr terms strongly dominate the filamentation dynamics (ξ > 10) at all wavelengths above λ ∼400 nm in argon and above λ ∼600 nm in air, although, due to the thresholds induced by the steps in photon numbers required to ionize oxygen (See Equation ( 10)), the evolution of this behavior is not strictly monotonic. Due to the domination of the higher-order Kerr terms, the latter will govern the intensity within the filaments, so that the ionization is mostly decoupled from the filamentation dynamics.

It should be noted that Miller formulae are sometimes considered to underestimate dispersion [32]. However, such correction to the dispersion curve of higher-order Kerr terms would result in a larger absolute value of the high-order Kerr indices in the UV. In this case, I ∆n Kerr =0 will be even lower in the UV. In other words, the curves of Figure 3 will decrease faster on the left side of the graph. As a consequence, the higher-order Kerr indices will have an even more dominant contribution to the self-guiding, as compared to that of plasma. Such larger dispersion would therefore reinforce qualitatively our conclusion about the domination of defocusing higher-order Kerr terms over the plasma defocusing.

This new vision of filamentation provides straightforward interpretation to experimental observations that the spectral broadening mostly occurs at the beginning of the filaments, while the spectrum is little affected in the main region of self-guided propagation [33]. This is due to the fact that, in the self-guided propagation, the intensity is clamped close to I ∆n Kerr =0 , so that the spectral counterpart of this Kerr effect, self-phase modulation (SPM), is also waved out. The earlier onset of filamentation for longer wavelengths is compatible with the Marburger formula [34], which predicts that the non-linear focal length describing self-focusing is inversely proportional to the wavelength. Furthermore, the longer filaments in the infrared appears to stem from the lower peak electron density (Figure 4(a)).

The very smooth dispersion curve of both air and argon above 500 nm [21] results in a very slow variation of this clamping intensity I ∆n Kerr =0 (Figure 3) and explains the quasi-constant clamping intensity observed over this spectral range.

The availability, for the first time, of simulations at constant reduced power P/P cr over a broad spectral range allows to discuss the choice of wavelength to optimize the filaments properties for specific purposes. As described above, the spectral dependence of the electron generation contrasts strongly with the common expectation that, due to a more efficient ionization, ultraviolet wavelengths should ionize the propagation medium more efficiently.

However, the peak electron density is not directly relevant for typical atmospheric applications. For example, laser-assisted water condensation [35], can be expected to require the largest possible value of the total generated charge. This total charge is obtained by integrating the plasma density over the filament length and cross-section (Figure 4(b)). Here, the longer filaments in the infrared as well as their larger diameter result in an unanticipated larger total charge at longer wavelengths.

Applications such as lightning control [36] require the longest possible filaments with the higher conductivity, i.e. a high longitudinal (transversely integrated) electron density.

Long wavelengths simultaneously optimize both of these properties (Figure 4(c,d)). In that regard, UV lasers providing short filaments with a small diameter and decreasing transverseintegrated electron densities would expectedly be less efficient than the commonly used Ti:Sa lasers around 800 nm, while wavelengths further in the IR should be even more efficient. 10 400 600 800 1000 1200 1400 1600 10 Infrared is also very attractive because it would alllow to work in the "telecom" spectral region (1.55 µm), where optical components are available and eye-safety standards are much more favorable for atmospheric applications than in the rest of the NIR and visible spectral region.

In conclusion, applying generalized Miller formulae to estimate arbitrary-order nonlinearities from the infrared to the ultraviolet spectrum, we have shown that higher-order nonlinear indices (up to n 8 in air and n 10 in argon) have a dominant contribution to both the focusing and defocusing terms implied in the self-guiding of 30 fs laser pulses in air, at all wavelengths between 300 and 1600 nm. As a consequence, the plasma generation is almost decoupled from the self-guiding of filaments over the whole visible and infrared spectral range. Instead, filaments can be considered as a self-guiding regime mostly governed in air and argon by the balance between the alternate signs of the nonlinear indices, respectively resulting in Kerr self-focusing and self-defocusing.

Moreover, a systematic investigation at constant reduced power P/P cr as a function of wavelength provides for the first time hints to choose optimal wavelengths for generating filaments optimized for a specific applications. In particular, we have shown that, contrary to previous expectations, the infrared is more favorable than the commonly used 800 nm wavelength if long ionized filaments or high total amount of charges are required. This raises the hope to further improve the spectacular results [5,35,36] recently obtained with Titanium:Sapphire lasers. Moreover, the higher eye-safety threshold in the telecom window at 1.55 µm is favorable for the practical development of the evisioned applications in free space.

FIG. 1 :

 1 FIG. 1: Maximum on-axis intensity (a,b), electron density (c,d), spectral broadening (e,f) and pulse-averaged ratio ξ of the on-axis pulse-averaged contributions of the higher-order Kerr and plasma contributions to the non-linear refractive index (g,h; see text for details), as a function of the wavelength and propagation distance in air (a,c,e,g) and argon (b,d,f,h).

FIG. 2 :FIG. 3 :

 23 FIG.2: Wavelength dependence close to 800 nm of the electron density generated by a 30 fs pulse of constant intensity 50 TW

1 )FIG. 4 :

 14 FIG. 4: Wavelength dependence of ionization in laser filamentation. (a) Peak electron density; (b) total number of electrons; (c,d) Transverse-integrated longitudinal electron density in air and argon, representative of the electric conductivity of the filament. Note the difference with Figures 1(c,d), which is due to the larger filament diameter in the infrared.

Acknowledgements. This work was supported by the Conseil Régional de Bourgogne, the ANR COMOC, the FASTQUAST ITN Program of the 7th FP and the Swiss NSF (contracts 200021-116198 and 200021-125315).


Georges Charpak

Patrick Benaben

Philippe Breuil

Paolo Martinengo

Eugenio Nappi

Vladimir Peskov
email: vladimir.peskov@cern.ch

Results from prototypes of environmental and health alarm devices based on gaseous detectors operating in air in counting mode

Keywords: Gaseous detectors, Rn detection, Detection of dangerous gases

à la diffusion de documents scientifiques de niveau recherche, publiés ou non, émanant des établissements d'enseignement et de recherche français ou étrangers, des laboratoires publics ou privés.

I. Introduction

Environmental alarm, monitoring and health safety devices operating in air in ionization mode are commercially available: for example smoke detectors, sensors of dangerous gases, medical X-ray devices and charged particle dosimeters. The sensitivity of these detectors is mainly determined by the sensitivity of compact pico-amperemeters mounted inside the devices (typically ∼pA). In this work, we investigated the possibility to exploit the gaseous detectors in air in avalanche mode. In this case the gaseous detector will be a naturally integrated preamplifier for the electronic circuit, allowing to not only make the sensor simpler and cheaper, but in some cases also significantly increasing its sensitivity. In the following the first promising results obtained within this approach are presented.

Nuclear Instruments and Methods in Physics Research Section A: Accelerators, Spectrometers, Detectors and Associated Equipment, 2011, 628 [START_REF] Raether | Electron Avalanches and Breakdown in Gases[END_REF], 187-189, Proceedings of the 12 th International Vienna Conference on Instrumentation, doi:10.1016/j.nima.2010.06.313 2

II. Results

I II I. .1 1. . O

Op pe er ra at ti io on n o of f g ga as se eo ou us s d de et te ec ct to or rs s i in n a ai ir r It is well known that air is not a good quenching gas, and as a consequence of this the traditional gaseous detectors (single-wire and parallel-plate) suffer from instabilities, especially from photon feedback [START_REF] Raether | Electron Avalanches and Breakdown in Gases[END_REF]. For this reason, we have studied in our recent work [START_REF] Charpak | [END_REF] the operation in air of hole-type detectors in which, due to the avalanche confinement in the holes, the photon feedback is strongly reduced. Indeed, an exceptionally high gas gain could be achieved with these hole-type detectors; however, at air humidity above 70% they become noisy [START_REF] Charpak | [END_REF], due to the charge leak across the hole walls. In this work, we investigated the feasibility to use wire-type counters instead of the hole-type detectors. The main interest of using a wire detector is that there is practically no limit in the size of the dielectric interface between the cathode cylinder and the anode wire, thus allowing the implementation of rectangular grooves [3] to suppress surface leakage due to humidity. Moreover, as was shown in [3], geometrical optimization of the wire detectors can significantly reduce the photon feedback, and they become capable of operating stably at gas gains of 10 3 -10 4 . We used such optimized wire counters in several applications [3] and [4]. Below we will describe two of them: Rn detection and detection of some dangerous low ionization potential (LIP) gases in air. I II I. .2 2. . R Ra ad do on n d de et te ec ct to or r It is well known that Rn gas from the environment, accumulating in buildings, especially in the basements, represents a significant threat to human health. Our work, however, was not focused on health safety (which is quite well covered with the existing detectors), but on the on-line detection of Rn as a possible precursor of a forthcoming earthquake. Indeed, some recent studies have shown the possibility to correlate rapid changes of the Rn concentration in soil or in groundwater to the early prediction of earthquakes (see [3] and references therein). In order to verify such observations on a more solid statistical ground it is needed to create a wide network of cheap, compact and high sensitivity Rn detectors, deployed in key points where the earthquake may potentially occur. The existing excellent commercial detectors are too expensive to be employed in large numbers. Two types of detectors oriented towards this particular application were developed and tested in this work: a simple single-wire counter (SWC), extensively used for basic studies, and a more sophisticated detector, a multiwire proportional counter (MWPC). The schematic drawing of the SWC is shown in Figure 1, its cathode cylinder is 60 mm in diameter, and the anode wire is 100 μm in diameter. During the measurements a positive HV was applied to the anode wire whereas the outer cylinder was grounded. The signals from the anode wire were detected by a custom made charge-sensitive amplifier able to deal with long-rise-time pulses (due to the long drift time of the negative ions), and if necessary they were in addition amplified by a research amplifier. In most of the measurements the signals were analyzed and displayed by a Labview program. In Figure 2 a schematic drawing of the MWPC is shown. The outer cylinder, 40 mm in diameter and 50 cm long, was made of stainless steel (SS) or of a stainless steel mesh with anode and cathode wires inside, stretched parallel to the cylinder axis in a hexagonal arrangement. This design was actually an exact copy of the detector described in [5], and the same technology was used for the manufacturing. However for each anode wire, protective grooves (to minimize the charge leak across the surface) were implemented on both ends, at the top and the bottom dielectric flanges. In the measurements with alpha particles, only events with two or more wires producing signals within a gate of a few μs have been accepted and analyzed. As an example the signals, produced by a 241 Am source when the detector was filled with ambient air, are shown in Figure 3 4 as a function of the applied voltage, for different diameters of the anode wire. Both the SWC and the MWPC have a broad counting plateau [3] allowing to perform reliable measurements at various atmospheric conditions. The main results obtained with our air-filled detectors are summarized in Table 1, where the minimum detector activity (MDA) measured during different time intervals is reported. For comparison, the MDA for one of the best commercial Rn detectors, the Atmos [3], is also presented in the same table. As can be seen from this table, the MDA of the MWPC is as low as the MDA of the best commercial detector. With our detectors we could easily detect small Rn traces in air (see also [3] for more details).

+ = +

By measuring the photocurrent I from the ionization chamber, the concentration n of the dangerous gases can be determined solving the following equation:

{ } 0 exp( ( )) exp( ) / L I NQ K d x nx dx n σ σ = - + - ∫
where N is the number of photons emitted per second by the lamp placed at a distance d from the ionization chamber, Q is the quantum efficiency of the LIP gas, L is the length of the ionization chamber, K is the UV light absorption coefficient in air, and σ is the photo absorption cross-section of the LIP gas at the given UV wavelength. For the sake of simplicity, let us consider a particular case of a very low concentration of a LIP gas, and a UV wavelength at which the absorption in air is small, then n=I/NQnσL. Typically, the lowest concentration of the LIP gases which can be reliably detected with commercial photoionization sensors is in the range of 10-100 ppm. In paper [6] we already described a prototype of a photoionization detector for dangerous gases based on hole-type amplifiers which, due to the gas multiplication, allows to increase the sensitivity. In this work, we investigated if SWCs can be used instead of hole-type detectors, what may open up the possibility to exploit them in a humid atmosphere. The experimental setup used for these studies was basically the same as described in [6]. The small modifications were: the introduction of an additional large-volume buffer gas chamber, allowing for the preparation of the gas mixtures with very low concentrations of LIP gases, and the possibility of using a pulsed Ar lamp inside the test chamber. The measurements were performed either in current mode (continuous UV source combined with a compact SWC operating with a lower gas gain) or in pulse mode (pulsed lamp combined with SWC operating in pulse mode), see [Figure 5] and [Figure 6]. In the case of current measurements and small values of n and K, the concentration of the LIP gases can be calculated from the following formula: n=I/ANQnσL. As can be seen, for the given fixed lamp intensity the detection sensitivity is increased by a factor A.

In the case of pulse measurements, the integrated avalanche charge per lamp pulse emitting N p photons is: Δq=N p σnLQA. The main advantage of the pulse mode is the easy way of calibrating the gas gain: for example using the radioactive sources 241 Am (see Figure 3) and 55 Fe [3]. In Figure 6, as an example, are shown the signal amplitudes vs. the voltage, for the SWC operating in pulse mode and detecting various concentrations of benzene vapors. As can be seen, a benzene concentration as low as 0.03 ppm could be detected in air, what is 10-100 times better than the typical sensitivity of commercial photoionization detectors.

3 I

 3 II I. .3 3. . D De et te ec ct to or rs s f fo or r g ga as se es s w wi it th h a a l lo ow w i io on ni iz za at ti io on n p po ot te en nt ti ia al l ( (L LI IP P) ) Commercial photoionization detectors are working on the principle of ionizing LIP gases (benzene, toluene and others) by monochromatic UV radiation emitted from a lamp:

Figures 4 F

 4 Figures

  , and the mean amplitudes of the signals induced by alpha Nuclear Instruments and Methods in Physics Research Section A: Accelerators, Spectrometers, Detectors and Associated Equipment, 2011, 628(1), 187-189, Proceedings of the 12 th International Vienna Conference on Instrumentation, doi:10.1016/j.nima.2010.06.313 particles are depicted in Figure

  Instruments and Methods in Physics Research Section A: Accelerators, Spectrometers, Detectors and Associated Equipment, 2011, 628(1), 187-189, Proceedings of the 12 th International Vienna Conference on Instrumentation, doi:10.1016/j.nima.2010.06.313 6

	wi it th h a a S SW WC C o op pe er ra at ti in ng g i in n a ai ir r a an nd d i ir rr ra ad di ia at te ed d w wi it th h a a 241 241 A Am m s so ou ur rc ce e. . T Th he e l la ar rg ge e
	p pu ul ls se es s w we er re e p pr ro od du uc ce ed d b by y a al lp ph ha a p pa ar rt ti ic cl le es s w wh he er re ea as s t th he e s sm ma al ll l o on ne es s w we er re e c ca au us se ed d b by y 6 60 0 k ke eV V
	F Fi ig gu ur re e 4 4: : M Me ea an n s si ig gn na al l a am mp pl li it tu ud de e p pr ro od du uc ce ed d b by y a al lp ph ha a p pa ar rt ti ic cl le es s v vs s. . t th he e v vo ol lt ta ag ge e a ap pp pl li ie ed d t to o d de et te ec ct to or rs s h ha av vi in ng g a a
	c ca at th ho od de e d di ia am me et te er r o of f 6 60 0 m mm m a an nd d d di if ff fe er re en nt t d di ia am me et te er rs s f fo or r t th he e a an no od de e w wi ir re es s. .
	m mo od de e, , o or r a at t a a g ga ai in n o of f 3 3; ; a at t c c∼ ∼0 0. .0 03 3 p pp pm m t th he e g ga as s g ga ai in n d du ur ri in ng g t th he e m me ea as su ur re em me en nt ts s w wa as s i in nc cr re ea as se ed d t to o ∼ ∼4 4× ×1 10 0 3 3 . .	r

Nuclear Instruments and Methods in Physics Research Section A: Accelerators, Spectrometers, Detectors and Associated Equipment, 2011, 628

[START_REF] Raether | Electron Avalanches and Breakdown in Gases[END_REF]

, 187-189, Proceedings of the 12 th International Vienna Conference on Instrumentation, doi:10.1016/j.nima.2010.06.313 5 F Fi ig gu ur re e 3 3: : T Ty yp pi ic ca al l s si ig gn na al ls s m me ea as su ur re ed d w Nuclear F Fi ig gu ur re e 5 5: : G Ga ai in n v vs s. . a ap pp pl li ie ed d v vo ol lt ta ag ge e c cu ur rv ve es s f fo or r t th he e S SW WC C o op pe er ra at ti in ng g i in n c cu ur rr re en nt t m mo od de e ( (o op pe en n t tr ri ia an ng gl le es s a an nd d f fi il ll le ed d r rh ho om mb bu us se es s) ) a an nd d i in n p pu ul ls se e m mo od de e ( (o op pe en n s sq qu ua ar re es s) ). . T Th he e t tr ri ia an ng gl le es s r re ep pr re es se en nt t m me ea as su ur re em me en nt ts s w wi it th h 1 10 00 0 p pp pm m e et th hy yl lf fe er ro ov ve en ne e v va ap po or rs s ( (t th he e U UV V l li ig gh ht t d do oe es s n no ot t h hi it t t th he e S SW WC C c ca at th ho od de e) ). . T Th he e r rh ho om mb bu us se es s a an nd d s sq qu ua ar re es s a ar re e t th he e g ga ai in n c ca al li ib br ra at ti io on n c cu ur rv ve es s m me ea as su ur re ed d u us si in ng g a a s su ur rf fa ac ce e p ph ho ot to oe ef ff fe ec ct t f fr ro om m t th he e c ca at th ho od de e ( (f fo or r t th he e p pu ur rp po os se e o of f t th he es se e p pa ar rt ti ic cu ul la ar r m me ea as su ur re em me en nt ts s t th he e c ca at th ho od de e w wa as s e ex xp po os se ed d t to o t th he e l la am mp p l li ig gh ht t) ). . F Fi ig gu ur re e 6 6: : S Si ig gn na al l v vs s. . v vo ol lt ta ag ge e c cu ur rv ve es s f fo or r t th he e S SW WC C o op pe er ra at ti in ng g i in n p pu ul ls se e m mo od de e a an nd d d de et te ec ct ti in ng g v va ar ri io ou us s c co on nc ce en nt tr ra at ti io on ns s o of f b be en nz ze en ne e. . A At t a a b be en nz ze en ne e c co on nc ce en nt tr ra at ti io on n c c= =1 10 00 0 p pp pm m t th he e m me ea as su ur re em me en nt ts s w we er re e p pe er rf fo or rm me ed d e ei it th he er r i in n i io on ni iz za at ti io on n c ch ha am mb be er

Nuclear Instruments and Methods in Physics Research Section A: Accelerators, Spectrometers, Detectors and Associated Equipment, 2011, 628(1), 187-189, Proceedings of the 12 th International Vienna Conference on Instrumentation, doi:10.1016/j.nima.2010.06.313