Alexander Khrabrov

Validation and benchmarking of two particle-in-cell codes for a glow discharge

The two particle-in-cell codes EDIPIC and LSP are bench-marked and validated for a parallel-plate glow discharge in helium, in which the axial electric field had been carefully measured, primarily to investigate and improve the fidelity of their collision models. The scattering anisotropy of electron-impact ionization, as well as the value of the secondary-electron emission yield, are not well known in this case. The experimental uncertainty for the emission yield corresponds to a factor of two variation in the cathode current. If the emission yield is tuned to make the cathode current computed by each code match the experiment, the computed electric fields are in excellent agreement with each other, and within about 10% of the experimental value. The non-monotonic variation of the width of the cathode fall with the applied voltage seen in the experiment is reproduced by both codes. The electron temperature in the negative glow is within experimental error bars for both codes, but the density of slow trapped electrons is underestimated. A more detailed code comparison done for several synthetic cases of electron-beam injection into helium gas shows that the codes are in excellent agreement for ionization rate, as well as for elastic and excitation collisions with isotropic scattering pattern. The remaining significant discrepancies between the two codes are due to differences in their electron binary-collision models, and for anisotropic scattering due to elastic and excitation collisions.

Electron scattering in helium for Monte Carlo simulations

An analytical approximation for differential cross-section of electron scattering on helium atoms is introduced. It is intended for Monte Carlo simulations, which, instead of angular distributions based on experimental data (or on first-principle calculations), usually rely on approximations that are accurate yet numerically efficient. The approximation is based on the screened-Coulomb differential cross-section with energy-dependent screening. For helium, a two-pole approximation of the screening parameter is found to be highly accurate over a wide range of energies.

Self-amplification of electrons emitted from surfaces in plasmas with E × B fields

Emission from surfaces is known to cause enhanced wall heating and enhanced energy loss from plasma electrons. When E × B fields are present, emitted electrons are heated by the drift motion and cause enhanced transport along E. All emission effects are normally predicted to reach a maximum when the sheath becomes space-charge limited because any ‘additional’ emitted electrons return to the wall. But the returning electrons are also heated in the E × B drift, further enhancing transport, and return to the wall with extra energy, further enhancing the energy flux. Returning electrons can gain enough energy to induce secondaries, thereby self-amplifying to higher intensities. This newly analyzed mechanism could affect the wall heating, transport and global energy balance under certain conditions. Theory and simulations are presented.

Investigation of the Paschen curve for helium in the 100–1000 kV range

The left branch of the Paschen curve for helium gas is studied both experimentally and by means of particle-in-cell/Monte Carlo collision (PIC/MCC) simulations. The physical model incorporates electron, ion, and fast atom species whose energy-dependent anisotropic scattering on background neutrals, as well as backscattering at the electrodes, is properly accounted for. For the range of breakdown voltage 15 kV≤Vbr≤130 kV, a good agreement is observed between simulations and available experimental results for the discharge gap d = 1.4 cm. The PIC/MCC model is used to predict the Paschen curve at higher voltages up to 1 MV, based on the availability of input atomic data. We find that the pd similarity scaling does hold and that above 300 kV, the value of pd at breakdown begins to increase with increasing voltage. To achieve good agreement between PIC/MCC predictions and experimental data for the Paschen curve, it is essential to account for impact ionization by fast atoms (produced in charge exchange) and ions and for anisotropic scattering of all species on background atoms. With the increase of the applied voltage, energetic fast atoms progressively dominate in the overall ionization rate. The model makes this clear by predicting that breakdown would occur even without electron- and ion-induced ionization of the background gas, due to ionization by fast atoms backscattered at the cathode, and their high production rate in charge exchange collisions. Multiple fast neutrals per ion are produced when the free path is small compared to the electrode gap.The left branch of the Paschen curve for helium gas is studied both experimentally and by means of particle-in-cell/Monte Carlo collision (PIC/MCC) simulations. The physical model incorporates electron, ion, and fast atom species whose energy-dependent anisotropic scattering on background neutrals, as well as backscattering at the electrodes, is properly accounted for. For the range of breakdown voltage 15 kV≤Vbr≤130 kV, a good agreement is observed between simulations and available experimental results for the discharge gap d = 1.4 cm. The PIC/MCC model is used to predict the Paschen curve at higher voltages up to 1 MV, based on the availability of input atomic data. We find that the pd similarity scaling does hold and that above 300 kV, the value of pd at breakdown begins to increase with increasing voltage. To achieve good agreement between PIC/MCC predictions and experimental data for the Paschen curve, it is essential to account for impact ionization by fast atoms (produced in charge exchange) and i...

Spatial symmetry breaking in single-frequency CCP discharge with transverse magnetic field

An independent control of the flux and energy of ions impacting on an object immersed in a plasma is often desirable for many industrial processes such as microelectronics manufacturing. We demonstrate that a simultaneous control of these quantities is possible by a suitable choice of a static magnetic field applied parallel to the plane electrodes in a standard single frequency capacitively coupled plasma device. Our particle-in-cell simulations show a 60% reduction in the sheath width (that improves control of ion energy) and a fourfold increase in the ion flux at the electrode as a consequence of the altered ion and electron dynamics due to the ambient magnetic field. A detailed analysis of the particle dynamics is presented, and the optimized operating parameters of the device are discussed. The present technique offers a simple and attractive alternative to conventional dual frequency based devices that often suffer from undesirable limitations arising from frequency coupling and electromagnetic effects.An independent control of the flux and energy of ions impacting on an object immersed in a plasma is often desirable for many industrial processes such as microelectronics manufacturing. We demonstrate that a simultaneous control of these quantities is possible by a suitable choice of a static magnetic field applied parallel to the plane electrodes in a standard single frequency capacitively coupled plasma device. Our particle-in-cell simulations show a 60% reduction in the sheath width (that improves control of ion energy) and a fourfold increase in the ion flux at the electrode as a consequence of the altered ion and electron dynamics due to the ambient magnetic field. A detailed analysis of the particle dynamics is presented, and the optimized operating parameters of the device are discussed. The present technique offers a simple and attractive alternative to conventional dual frequency based devices that often suffer from undesirable limitations arising from frequency coupling and electromagnetic effects.

Multi-dimensional kinetic simulations of instabilities and transport in EXB devices

Summary form only given. Various ExB devices such as Hall thrusters, helicon thrusters, Penning and magnetron discharges are subject to numerous instabilities that yield anomalous electron transport and affect operation of these devices. To understand the details of anomalous electron transport in ExB devices we have performed multi-dimensional kinetic simulations of plasma processes in a number of ExB discharges. Results of simulations are compared with experimental findings [1] as well as fluid simulations [2]. The LSP (Large-Scale Plasma) PIC-MCC code has been substantially modified to simulate several ExB configurations including Hall Thruster and Penning discharge [1]. To enable robust simulations of these discharges, we implemented a new electrostatic solver using the PETSc library interface; we added comprehensive collision models based on anisotropic scattering [3], implemented electron emission algorithms from the EDIPIC [4] code and modified the external electric circuit model. The customized code, PPPL-LSP, now successfully models low-temperature plasmas in multiple dimensions and can be run on hundreds of processor cores, with simulations resolving fast electron processes as well as reach steady state (on ion time scale) without scaling of cross sections or reducing ion mass. We have performed extensive verification and validation of the modified code. In particular, various instabilities in ExB devices were simulated for Penning and magnetron discharges. Initial 3D simulations of the cylindrical Hall thruster [5] were also performed.

Nonlocal kinetic theory of plasma discharges

Summary form only given. The purpose of the talk is to describe recent advances in nonlocal electron kinetics in low-pressure plasmas. Low-pressure discharges are widely used in industry as the main plasma sources for many applications including plasma processing, discharge lighting, plasma propulsion, particle beam sources and nanotechnology. Being partially-ionized, bounded, and weakly-collisional, the plasmas in these discharges demonstrate nonlocal electron kinetic effects, nonlinear processes in the sheaths, beam-plasma interaction, collisionless electron heating, etc. Such plasmas often have a non-Maxwellian electron velocity distribution function. The plethora of kinetic processes supporting the non-equilibrium plasma state is an invaluable tool, which can be used to adjust plasma parameters to the specific needs of a particular plasma application. We report on recent advances in nonlocal electron kinetics in low-pressure plasmas where a non-Maxwellian electron velocity distribution function was “designed” for a specific purpose: in dc discharges with auxiliary biased electrodes for plasma control, hybrid DC/RF magnetized and unmagnetized plasma sources, and Hall thruster discharges. We show using specific examples that this progress was made possible by synergy between full-scale particle-in-cell simulations, analytical models, and experiments. Examples of recent progress are described in Special Section of Physics of Plasmas “Electron kinetic effects in low temperature plasmas” [1] and Special Issue of Plasma Sources Science and Technology “Transport in B-fields in low-temperature plasmas” [2].

Plasma-wall interaction in presence of intense electron emission from walls

Summary form only given. There have been sufficient experimental and theoretical evidence that strong secondary electron emission (SEE) from the channel walls affects thruster operation. SEE enhances the heat losses to the walls and increases electron conductivity, which, consequently, degrades thruster performance [1]. The plasma-surface interaction in presence of strong thermionic or secondary electron emission has been studied theoretically and experimentally. The electron flux to the wall is determined by the electron velocity distribution function (EVDF) and by the sheath potential, which is set by ambipolar condition consistent with the EVDF and the wall emitting properties [2,3]. Nonlinear coupling between EVDF and sheath potential is responsible for a number of unusual phenomena. For example, we observed relaxation sheath oscillations [3]. We have shown that the criterion for instability is that the secondary electron emission coefficient of electrons with energy normal to the wall bordering the wall potential becomes larger than unity [4]. We observed new regime where all plasma electrons leave and are substituted by secondary electrons [5]. In this regime, there is practically no electric field in plasma and sheath, so that ions are not drawn to the wall, plasma electrons are not confined and the plasma potential is negative. Sheath instabilities influence the current balance, energy loss, cross-B-field transport and even the bulk plasma properties. We have performed modeling of asymmetric regime where walls have different emission properties [6,7].

Kinetic effects in hall plasma thrusters

The plasma-wall interaction in the presence of strong secondary electron or thermionic emission has been studied theoretically and experimentally both as a basic phenomenon and in relation to numerous plasma applications such as, for example, fusion devices and plasma propulsion. For Hall thrusters, existing fluid models predict that secondary electron emission (SEE) is strong enough to enhance electron energy losses at the walls. According to the kinetic simulations, the electron velocity distribution function in a collisionless thruster plasma is non-Maxwellian, anisotropic, and features beams of secondary electrons emitted from the walls.1,2 Under such conditions, the effects of SEE on the plasma can be substantially weaker than predicted by the fluid models. This talk will review previous and recent experimental results, including probe measurements in the Hall thruster with various wall materials, which support the predictions of the kinetic studies.3,4 It is also shown that the wall material properties affect the electron cross-field transport in the thruster discharge. We will also discuss how these results can help in implementation of highly efficient and stable plasma regimes of the Hall thrusters.

Nonlocal collisionless and collisional electron transport in low temperature plasmas

A distinctive property of partially ionized plasmas is that such plasmas are always in a non-equilibrium state: the electrons are not in thermal equilibrium with the neutral species and ions, and the electrons are also not in thermodynamic equilibrium within their own ensemble, which results in a significant departure of the electron velocity distribution function from a Maxwellian. These non-equilibrium conditions provide considerable freedom to choose optimal plasma parameters for applications, which make gas discharge plasmas remarkable tools for a variety of plasma applications, including plasma processing, discharge lighting, plasma propulsion, particle beam sources, and nanotechnology. Typical phenomena in such discharges include nonlocal electron kinetics, nonlocal electrodynamics with collisionless electron heating, and nonlinear processes in the sheaths and in the bounded plasmas. We report on recent advances in nonlocal electron kinetics in low-pressure plasmas, in the Hall thruster discharges1,2, and dc discharges with auxiliary biased electrodes for plasma control3. We show on specific examples that this progress was made possible by synergy between full scale particle-in-cell simulations, analytical models, and experiments.