Numerical simulations used for a validity check on the

Numerical simulations used for a validity check on the laser induced photodetachment diagnostic method in electronegative plasmas N. Oudini, F. Taccogna, A. Bendib, and A. Aanesland Citation: Physics of Plasmas (1994-present) 21, 063515 (2014); doi: 10.1063/1.4886144 View online: http://dx.doi.org/10.1063/1.4886144 View Table of Contents: http://scitation.aip.org/content/aip/journal/pop/21/6?ver=pdfcov Published by the AIP Publishing Articles you may be interested in Sheath formation criterion in magnetized electronegative plasmas with thermal ions Phys. Plasmas 20, 033506 (2013); 10.1063/1.4795297 The positive ion temperature effect in magnetized electronegative plasma sheath with two species of positive ions Phys. Plasmas 19, 102108 (2012); 10.1063/1.4759460 Numerical simulations of electrical asymmetry effect on electronegative plasmas in capacitively coupled rf discharge J. Appl. Phys. 109, 013308 (2011); 10.1063/1.3530626 Comparison between experiment and simulation for argon inductively coupled plasma Phys. Plasmas 16, 113502 (2009); 10.1063/1.3261836 Three point method to characterize low-pressure electronegative discharges using electrostatic probe Rev. Sci. Instrum. 80, 013502 (2009); 10.1063/1.3065089

This article is copyrighted as indicated in the article. Reuse of AIP content is subject to the terms at: http://scitation.aip.org/termsconditions. Downloaded to IP: 193.194.91.34 On: Tue, 01 Jul 2014 08:04:12

PHYSICS OF PLASMAS 21, 063515 (2014)

Numerical simulations used for a validity check on the laser induced photo-detachment diagnostic method in electronegative plasmas N. Oudini,1 F. Taccogna,2 A. Bendib,3 and A. Aanesland4 1

Laboratoire des plasmas de d echarges, Centre de D eveloppement des Technologies Avanc ees, Cit e du 20 Aout BP 17 Baba Hassen, 16081 Algiers, Algeria 2 Istituto di Metodologie Inorganiche e dei Plasmi, CNR, via Amendola 122/D, 70126 Bari, Italy 3 Laboratoire d’Electronique Quantique, Facult e de Physique, USTHB, El Alia BP 32, Bab Ezzouar 16111, Algiers, Algeria 4 Laboratoire de Physique des Plasmas (CNRS, Ecole Polytechnique, Sorbonne Universit es,  UPMC Univ Paris 06, Univ Paris-Sud), Ecole Polytechnique, 91128 Palaiseau Cedex, France

(Received 25 March 2014; accepted 17 June 2014; published online 30 June 2014) Laser photo-detachment is used as a method to measure or determine the negative ion density and temperature in electronegative plasmas. In essence, the method consists of producing an electropositive channel (negative ion free region) via pulsed laser photo-detachment within an electronegative plasma bulk. Electrostatic probes placed in this channel measure the change in the electron density. A second pulse might be used to track the negative ion recovery. From this, the negative ion density and temperature can be determined. We study the formation and relaxation of the electropositive channel via a two-dimensional Particle-In-Cell/Mote Carlo collision model. The simulation is mainly carried out in a Hydrogen plasma with an electronegativity of a ¼ 1, with a parametric study for a up to 20. The temporal and spatial evolution of the plasma potential and the electron densities shows the formation of a double layer (DL) confining the photo-detached electrons within the electropositive channel. This DL evolves into two fronts that move in the opposite directions inside and outside of the laser spot region. As a consequence, within the laser spot region, the background and photo-detached electron energy distribution function relaxes/thermalizes via collisionless effects such as Fermi acceleration and Landau damping. Moreover, the simulations show that collisional effects and the DL electric field strength might play a non-negligible role in the negative ion recovery within the laser spot region, leading to a two-temperature negative ion distribution. The latter result might have important effects in the determination of the negative ion density and temperature from laser photo detachment diagnostic. C 2014 AIP Publishing LLC. [http://dx.doi.org/10.1063/1.4886144] V I. INTRODUCTION

Negatives ions might provide very useful advantages for several applications, e.g., plasma etching,1 neutral beam injection system for controlled thermonuclear fusion2–4 (ITERNBI), and electric propulsion applications5 (PEGASES). As a consequence, the development of negative ion diagnostics is an important task. Bredin et al.6 developed a Langmuir probe analysis for high electronegativity a  nne > 100 (here, n- and ne are the negative ion and electron density, respectively) that determines both the negative ion density and temperature. For lower electronegativity, laser photo-detachment has been used as a diagnostic tool for negative ion density and temperature measurements.7 The photo-detachment diagnostic method consists of producing an electropositive channel (negative ion free region) via laser photo-detachment, e.g., h þ H  ! H þ e, within an electronegative plasma bulk. The laser pulsed with a duration of a few ns, intensity and energy chosen such as to ensure a fast and total destruction of negative ions within the illuminated region, without exciting atoms or producing photoionization.7 An electrostatic probe is located within the illuminated region to track the electron density evolution. Several authors studied experimentally7–11 and theoretically12–15 the laser photo-detachment diagnostic. The negative ion density can be determined from the significant increase of electron 1070-664X/2014/21(6)/063515/9/$30.00

density within the illuminated region. The use of two pulses photo-detachment method allows tracking the negative ion density recovery, and then deduce the negative ion temperature.7,9 Therefore, understanding the behavior of photodetached electrons is very important because it is directly related to the accuracy of the negative ion measurements. Despite of the frequent use of this method, the understanding of laser pulse effects on the electron energy distribution function (EEDF) remains poor and ambiguous. The energy of electrons produced by photo-detachment is determined by the difference between the laser photon energy (in this case h ¼ 2.33 eV), and the electron affinity of negative ion (EA ¼ 0.75 eV for hydrogen). The production of mono-energetic electrons affects significantly the electron background EDF, while often the EEDF is considered Maxwellian during and after the laser pulse duration.7,9,11 Photo-detachment is widely considered as an instantaneous process;14,15 while in the most frequent cases, the total destruction of negative ions under the laser pulse effect requires an interval of nanoseconds.7 This time scale has the same order of plasma oscillation period and of electrons transit time through the illuminated region. This work is devoted to study the dynamics, i.e., formation and relaxation, of an electropositive channel induced by

21, 063515-1

C 2014 AIP Publishing LLC V

This article is copyrighted as indicated in the article. Reuse of AIP content is subject to the terms at: http://scitation.aip.org/termsconditions. Downloaded to IP: 193.194.91.34 On: Tue, 01 Jul 2014 08:04:12

063515-2

Oudini et al.

a laser pulse with a two-dimension Particle-In-Cell with Monte-Carlo-Collisions Model (2D PIC-MCC). The evolution of plasma potential and particles density within the illuminated region and near vicinity of it is described. The effects of the laser on the EEDF and the relaxation of photodetached electrons are studied in detail. The 2D PIC-MCC model is briefly described in Sec. II. Results are illustrated in Sec. III and discussed in Sec. IV. A conclusion summarizing the main outcomes of this work is given in Sec. V.

Phys. Plasmas 21, 063515 (2014) TABLE I. Physical gas, laser, and plasma parameters used in the simulation. Simulation parameters Te ¼ 1 eV Ti ¼ 0.2 eV 1020 m3 300 K 3.1 mTorr 532 nm 13 ns 3 mm 50 mJ

Electron temperature at the injection Ion temperature at the injection Gas background density (Pure atomic H) Gas background temperature Background pressure Laser light Laser pulse duration Laser spot radius Rl Emitted energy per laser pulse

II. TWO-DIMENSIONAL PARTICLE-IN-CELL WITH MONTE-CARLO-COLLISIONS MODEL

The PIC-MCC16,17 method consists of calculating the trajectories of a large number of plasma macro-particles under their self-consistent electrostatic force field obtained from Poisson equation’s solution on a grid, where the charge particle is deposited. Collisions are included via Monte Carlo null collision method.18 In our model,19 macro-particles are injected in a slab from the boundaries of the simulated region (see Figure 1). The source terms of electrons e and Hþ and H ions are fixed in order to sustain a hydrogen plasma with an electronegativity a ¼ 1 and a total plasma density of 1016 m3. The initial velocity of macro-particles is taken from a half-Maxwellian distribution at a given temperature (in Table I all the plasma parameters used are summarized). Particles reaching the boundaries are deleted from the list of tracked particles. The neutral gas is considered as a fixed background of pure hydrogen atom with uniform density and temperature (see Table I). A second harmonic Nd-YAG laser with a wavelength of 532 nm and a pulse duration of 13 ns is injected at t ¼ 0. The emitted energy during this laser pulse is about 50 mJ with a photon beam with a radius of 3 mm. The power and photon density are assumed to be distributed uniformly (step function) both in time and space. The negative ion photo-detachment process, i.e., h þ H  ! H þ e, is then self-consistently tracked via a Monte Carlo Collision procedure. All the collisional processes with the corresponding computed frequencies are listed in Table II. Standard requirements are followed for time step and grid cell size in order to guarantee stability and accuracy.16 The number of cells is 300  300, while the time step

is 1011 s and each species is simulated with, at least, 4  106 particles in the entire domain. A run with a larger computational domain of 2  2 cm2 (in order to reduce the influence of the boundaries) and 200 particles by cells per species (in order to reduce the numerical noise) has produced an electron relaxation time within 5% that resulted with X  Y ¼ 1  1 cm2. The error is smaller than any diagnostics device precision. The results presented in this work during the first 20 ns are instantaneous data (neither spatial smoothing nor temporal averaging are used), while the results presented after 20 ns are averaged over 100 time steps. III. NUMERICAL RESULTS A. General behavior

Figure 2(a) shows the temporal evolution of electron, positive and negative ion densities calculated at the center of the illuminated region during the first 20 ns. It appears that, under the effect of the laser pulse, negative ions are quickly converted into electrons and neutral atom: 2 ns illumination seems sufficient to remove almost all negative ions in the spot region. Thus, this region can be considered as an electropositive channel, since the electron density becomes almost equal to the positive ion density. After the first 2 ns, the electron density reaches a plateau and remains constant even after the laser pulse, while positive ion density is unchanged during this time scale. TABLE II. Collisional processes considered in the model and computed frequencies (averaged over the computational domain) calculated for conditions summarized in Table I.

Collisional mechanisms

Reactions

Frequency (s1)

References

Elastic scattering Excitation Ionization Electron detachment Mutual (ion-ion) neutralization Associative detachment Non associative detachment Charge exchange Photodetachment

eþH !eþH e þ H ! e þ H e þ H ! 2e þ Hþ e þ H ! 2e þ H H  þ H þ ! 2H

3.6  106