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This paper presents a technique for reconstructing the temporal evolution of ion distribution functions (IDF) in a Hall thruster using ion currents measured with a retarding potential analyzer. The method involves averaging discharge oscillations with temporal realignment based on the maxima of the discharge current. This technique was applied to ion currents from the experimental ID-Hall 2 thruster, successfully reconstructing the time-dependent ion distribution function in quasi-periodic plasma oscillation regimes. The results indicate that deformations in the integrated ion distribution function can be attributed to the IDF's temporal evolution over a characteristic time equal to the breathing mode oscillation period. This finding suggests the possibility of uncoordinated displacement of ionization and acceleration zones within the discharge. In certain oscillation regimes, the oscillations in ion transit time also appear to have a minor effect on ion acceleration. [ABSTRACT FROM AUTHOR]

This Perspective paper deals with an overview of particle-in-cell/Monte Carlo collision models applied to different plasma-propulsion configurations and scenarios, from electrostatic (E × B and pulsed arc) devices to electromagnetic (RF inductive, helicon, electron cyclotron resonance) thrusters, as well as plasma plumes and their interaction with the satellite. The most important items related to the modeling of plasma–wall interaction are also presented. Finally, the paper reports new progress in the particle-in-cell computational methodology, in particular, regarding accelerating computational techniques for multi-dimensional simulations and plasma chemistry Monte Carlo modules for molecular and alternative propellants. [ABSTRACT FROM AUTHOR]

In this Tutorial, we consider plasma sources with applications to fusion devices and high energy accelerators. These ion sources typically produce negative ions from hydrogen-isotope gases, which are extracted through one or multiple apertures and accelerated to high kinetic energies. Next, they are either double stripped of two electrons to form positive ions used as precursors in accelerator devices or neutralized to produce a neutral beam injected in tokamak reactors. Contrary to the working conditions of most ion sources where volume production prevails, the mechanism of negative ion production by dissociative electron attachment on vibrationally excited molecules inside the plasma volume of fusion-type hydrogen-fueled high power discharges is mostly balanced by their destruction by detachment before being extracted rendering this means of producing negative ions rather inefficient. Surface production through the transfer of electrons from low work function metallic materials to the impacting atoms is the alternative solution to fulfill the requirements for the applications concerned. Negative ions are produced close to the aperture from which they are extracted. As a result, the analysis and understanding of the extraction mechanisms through experimental diagnostics is rather difficult due to the lack of accessibility and can only give a partial view. In addition, most of the experimental work is focused on the validation of requirements for the applications and not to the investigation of the fundamental processes that take place inside these types of sources. This Tutorial is focused on the description and understanding of the physical mechanisms behind the extraction and acceleration of negative ions from hydrogen plasma sources through modeling methods. We describe the numerical techniques of particle-based methods with a specific emphasis on particle-in-cell Monte Carlo collision algorithms. An analysis of the physical processes involved in driving the negative ions from the plasma source, across the apertures and inside the accelerator as reported in the literature, is presented in detail. This Tutorial concludes with additional and future works to be addressed in the coming years. [ABSTRACT FROM AUTHOR]

The use of sparse particle-in-cell (PIC) algorithms to accelerate the standard explicit PIC scheme has recently been successfully applied in the context of single-frequency capacitively coupled plasma discharges [Garrigues et al., J. Appl. Phys. 129, 153303 (2021)]. We have extended the sparse PIC scheme to model dual-frequency capacitive discharges. Comparisons between standard and sparse PIC algorithms show that the plasma properties as well as the electron and ion distribution functions can be retrieved with a maximum error of 2%. This work opens the interest of using the sparse PIC algorithm to perform 2D and 3D simulations under real operating conditions of capacitively coupled plasma discharges. [ABSTRACT FROM AUTHOR]

In Paper I [Garrigues et al., Phys. Plasmas 31, 073907 (2024)], we have extended the sparse PIC approach already used in the literature with the offset scheme to reduce the grid-based error. In this study, we demonstrate the ability of the offset sparse PIC algorithm to model partially magnetized low-temperature plasmas by reducing the grid-based error. In the context of multi-cusp magnetic field configurations, the offset scheme reduces the error of the current collected at the walls to less than 5 % for more of the plasma conditions encountered in ion source applications. The formation of a double layer in the sheath region is also captured. In the context of the electron drift instability that occurs in the Hall thruster, the plasma properties as well as the ion velocity distribution function can be retrieved with a high enough precision without considering an initial regular grid with a smaller mesh resolution. The results also highlight the advantage of combining the electric potential at the nodes of the regular grid instead of directly combining the electric field from the component grids. Compared to the regular PIC algorithm, the typical speed-up factor is about three for a number of mesh nodes of 256 2 and five for 512 2 . [ABSTRACT FROM AUTHOR]

Hall thrusters are E × B plasma devices characterised by a large azimuthal electron current, which is involved in the formation of a wide variety of instabilities on different frequency scales (from kilohertz to gigahertz) and propagating in different directions. We have focused on a limited number of low-frequency instabilities that could be experimentally observed, such as breathing mode (BM) and ion transit time oscillations (ITTO). There are still gray areas in the understanding of the mechanisms behind these instabilities, which are often described individually, without considering an eventual exchange of information between the different types of instability. A wavelet time-frequency study of the plasma revealed the coexistence and interdependence of distinct instabilities. We suspect a possible interaction between the breathing mode and higher-frequency oscillations leading to ITTOs: it was shown that a transition occurred when the frequency of one of the BM harmonics became a multiple of the frequency of the higher-frequency oscillations. This was also accompanied by a deformation of the ion energy distribution functions. [ABSTRACT FROM AUTHOR]

Experimental results are reported from two measurement techniques (semiconductor switching and electro-optic sampling) that allow temporal characterization of electron bunches produced by a laser-driven plasma-based accelerator. As femtosecond electron bunches exit the plasma-vacuum interface, coherent transition radiation (at THz frequencies) is emitted. Measuring the properties of this radiation allows characterization of the electron bunches. Theoretical work on the emission mechanism is represented, including a model that calculates the THz waveform from a given bunch profile. It is found that the spectrum of the THz pulse is coherent up to the 200 mu m thick crystal (ZnTe) detection limit of 4 THz, which corresponds to the production of sub-50 fs (root-mean-square) electron bunch structure. The measurements demonstrate both the shot-to-shot stability of bunch parameters that are critical to THz emission (such as total charge and bunch length), as well as femtosecond synchrotron between bunch, THz pulse, and laser beam.

Enhanced electron trapping using plasma density down ramps as a method for improving the performance of laser injection schemes is proposed and analyzed. A decrease in density implies an increase in plasma wavelength, which can shift a relativistic electron from the defocusing to the focusing region of the accelerating wakefield, and a decrease in wake phase velocity, which lowers the trapping threshold. The specific method of two-pulse colliding pulse injector was examined using a three-dimensional test particle tracking code. A density down-ramp with a change of density on the order of tens of percent over distances greater than the plasma wavelength led to an enhancement of charge by two orders in magnitude or more, up to the limits imposed by beam loading. The accelerated bunches are ultrashort (fraction of the plasma wavelength, e.g., ~; 5 fs), high charge (> 20 pC at modest injection laser intensity 10^17 W/cm^2), with a relative energy spread of a few percent at a mean energy of ~; 25 MeV, and a normalized root-mean square emittance on the order 0.5 mm mrad.

The temporal pro le of relativistic laser-plasma-accelerated electron bunches has been characterized. Coherent transition radiation at THz frequencies, emitted at the plasma-vacuum boundary, is measured through electro-optic sampling. The data indicates that THz radiation is emitted by a skewed bunch with a sub-50 fs rise time and a ~; 600 fs tail (half-width-at-half-maximum), consistent with ballistic debunching of 100 percent-energy-spread beams. The measurement demonstrates both shot-to-shot stability of the laser-plasma accelerator and femtosecond synchronization between bunch and probe beam.

An injection scheme for a laser wakefield accelerator that employs a counterpropagating laser (colliding with the drive laser pulse, used to generate a plasma wake) is discussed. The threshold laser intensity for electron injection into the wakefield was analyzed using a heuristic model based on phase-space island overlap. Analysis shows that the injection can be performed using modest counterpropagating laser intensity a_1 < 0.5 for a drive laser intensity of a_0 = 1.0. Preliminary experiments were preformed using a drive beam and colliding beam. Charge enhancement by the colliding pulse was observed. Increasing the signal-to-noise ratio by means of a preformed plasma channel is discussed.

An electron injector concept that uses a single injection laser pulse colliding with a pump laser pulse in a plasma is analyzed. The pump pulse generates a large amplitude laser wakefield (plasma wave). The counter propagating injection pulse collides with the pump laser pulse to generate a beat wave with a slow phase velocity. The ponderomotive force of the slow beat wave is responsible for injecting plasma electrons into the wakefield near the back of the pump pulse. Test particle simulations indicate that significant amounts of charge can be trapped and accelerated ( ~; 10 pC). For higher charge, beam loading limits the validity of the simulations. The accelerated bunches are ultrashort ( ~; 1 fs) with good beam quality (relative energy spread of a few percent at a mean energy of ~; 10 MeV and a normalized rms emittance on the order 0.4 mm.mrad). The effects of interaction angle and polarization are also explored, e.g., efficient trapping can occur for near-collinear geometries. Beat wave injection using a single injection pulse has the advantages of simplicity, ease of experimental implementation, and requires modest laser intensity I = 8.8 x 1017 W/cm^ 2.

Coherent terahertz and millimeter wave radiation from laser accelerated electron bunches has been measured. The bunches were produced by tightly focusing (spot diameter ~; 6 mu m) a high peak power (up to 10W), ultra-short (>50 fs) laser pulse from a high repetition rate (10 Hz) laser system (0.8 mu m), onto a high density (>1019 cm3) pulsed gas jet of length ~; 1.5 mm. As the electrons exit the plasma, coherent transition radiation is generated at the plasma-vacuum boundary for wavelengths long compared to the bunch length. Radiation in the 0.3 -19 THz range and at 94 GHz has been measured and found to depend quadratically on the bunch charge. The measured radiated energy for two different collection angles is in good agreement with theory. Modeling indicates that optimization of this table-top source could provide more than 100 mu J/pulse. Together with intrinsic synchronization to the laser pulse, this will enable numerous applications requiring intense terahertz radiation. This radiation can also be used as a powerful tool for measuring the properties of laser accelerated bunches at the exit of the plasma accelerator. Preliminary spectral measurements indicates that bunches as short as 30 - 50 fs have been produced in these laser driven accelerators.

Plasma density down-ramps are proposed as a method for improving the performance of laser injection schemes. A decrease in density implies an increase in plasma wavelength, which can shift a relativistic electron from the defocusing to the focusing region of the accelerating wakefield. Also, a decrease in density leads to a decrease in wake phase velocity, which lowers the trappingthreshold. The specific method of two-pulse colliding pulse injector was examined using a 3D test particle tracking code. A density down-ramp of 30% led to an order of magnitude enhancement of the trapping fraction compared to the uniform plasma case, without degrading other bunch properties.

Coherent THz radiation was produced from relativistic electron bunches of subpicosecond duration. The electron beam was produced by strongly focused (approx. equal to 6 mu-m), high peak power (up to 10 TW), ultra-short (> or = to 50 fs) laser pulses of a 10 Hz repetition rate Ti:sapphire chirped pulse amplification (CPA) laser system via self-modulated laser wakefield acceleration (SM-LWFA) in a high density (> 1019 cm-3) pulsed gas jet. As the electrons exit the plasma, coherent transition radiation is generated at the plasma-vacuum boundary for wavelengths long compared to the bunch length. Radiation yield in the 0.3 to 19 THz range and at 94 GHz has been measured and found to depend quadratically on the bunch charge. The measured total radiated energy in the THz range for two different collection angles is in good agreement with theory. Modeling indicates that optimization of this table-top source could provide more than 100 mu-J/pulse. Together with intrinsic synchronization to the laser pulse, this will enable numerous applications requiring intense terahertz radiation. This radiation can also be applied as a useful tool for measuring the properties of laser accelerated bunches at the exit of the plasma accelerator.

Coherent radiation in the 0.3 - 3 THz range has been generated from femto second electron bunches at a plasma-vacuum boundary via transition radiation. The bunches produced by a laser-plasma accelerator contained 1.5 nC of charge. The THz energy per pulse within a limited 30 mrad collection angle was 3.5 nJ and scaled quadratically with bunch charge, consistent with coherent emission. Modeling indicates that this broadband source produces about 0.3 muJ per pulse within a 100 mrad angle, and that increasing the transverse plasma size and electron beam energy could provide more than 100 muj/pulse.

A 10 Hz, 10 TW solid state laser system has been used to produce electron beams suitable for radio-isotope production. The laser beam was focused using a 30 cm focal length f/6 off-axis parabola on a gas plume produced by a high pressure pulsed gas jet. Electrons were trapped and accelerated by high gradient wakefields excited in the ionized gas through the self-modulated laser wakefield instability. The electron beam was measured to contain excesses of 5 nC/bunch. A composite Pb/Cu target was used to convert the electron beam into gamma rays which subsequently produced radio-isotopes through (gamma, n) reactions. Isotope identification through gamma-ray spectroscopy and half-life time measurements demonstrated that Cu^61 was produced which indicates that 20-25 MeV gamma rays were produced, and hence electrons with energies greater than 25-30 MeV. The production of high energy electrons was independently confirmed using a bending magnet spectrometer. The measured spectra had an exponential distribution with a 3 MeV width. The amount of activation was on the order of 2.5 uCi after 3 hours of operation at 1 Hz. Future experiments will aim at increasing this yield by post-accelerating the electron beam using a channel guided laser wakefield accelerator.

Three-dimensional simulations of partially magnetized plasma are real challenges that actually limit the understanding of the discharge operations such as the role of kinetic instabilities using explicit Particle-In-Cell (PIC) schemes. The transition to high performance computing cannot overcome all the limits inherent to very high plasma densities and thin mesh sizes employed to avoid numerical heating. We have applied a recent method proposed in the literature [L. F. Ricketson and A. J. Cerfon, Plasma Phys. Controlled Fusion 59, 024002 (2017)] to model low temperature plasmas. This new approach, namely, the sparse grid combination technique, offers a gain in computational time by solving the problem on a reduced number of grid cells, hence allowing also the reduction of the total number of macroparticles in the system. We have modeled the example of the two-dimensional electron drift instability, which was extensively studied in the literature to explain the anomalous electron transport in a Hall thruster. Comparisons between standard and sparse grid PIC methods show an encouraging gain in the computational time with an acceptable level of error. This method offers a unique opportunity for future three-dimensional simulations of instabilities in partially magnetized low temperature plasmas. [ABSTRACT FROM AUTHOR]

The use of a particle-in-cell (PIC) algorithm with an explicit scheme to model low temperature plasmas is challenging due to computational time constrains related to resolving both the electron Debye length in space and the inverse of a fraction of the plasma frequency in time. One recent publication [Ricketson and Cerfon, Plasma Phys. Control. Fusion 59, 024002 (2017)] has demonstrated the interest of using a sparse grid combination technique to accelerate the explicit PIC model. Simplest plasma conditions were considered. This paper is the demonstration of the capability and the effectiveness of the sparse grid combination technique embedded in the PIC algorithm (hereafter called "sparse PIC") to self-consistently model capacitively coupled radio frequency discharges. For two-dimensional calculations, the sparse PIC approach is shown to accurately reproduce the plasma profiles and the energy distribution functions compared to the standard PIC model. The plasma parameters obtained by these two numerical methods differ by less than 5%, while a speed up in the executable time between 2 and 5 is obtained depending on the setup. [ABSTRACT FROM AUTHOR]

The Particle-In-Cell Monte Carlo Collision (PIC MCC) method has been used by different authors in the last ten years to describe negative ion extraction in the context of neutral beam injection for fusion. Questionable results on the intensity and profile of the extracted negative ion beamlets have been presented in several recently published papers. Using a standard explicit PIC MCC method, we show that these results are due to a non-compliance with the constraints of the numerical method (grid spacing, number of particles per cell) and to a non-physical generation of the simulated plasma. We discuss in detail the conditions of mesh convergence and plasma generation and show that the results can significantly deviate from the correct solution and lead to unphysical features when the constraints inherent to the method are not strictly fulfilled. This paper illustrates the importance of verification in any plasma simulation. Since the results presented in this paper have been obtained with careful verification of the method, we propose them as benchmarks for future comparisons between different simulation codes for negative ion extraction. [ABSTRACT FROM AUTHOR]