Peter Hartmann

• PhD
• Senior Researcher at Wigner Research Centre for Physics of the Hungarian Academy of Sciences

The PlasmaKristall-4 (PK-4) experiment on the International Space Station allows for the study of the three-dimensional interaction between plasma and dust particles. Previous simulations of the PK-4 environment have discovered fast moving ionization waves in the dc discharge [Hartmann et al., Plasma Sources Sci. Technol. 29, 115014 (2020)]. These...

We present a method for the in-situ determination of the effective secondary electron emission coefficient (SEEC, γ) in a capacitively coupled plasma (CCP) source based on the γ-dependence of the DC self-bias voltage that develops over the plasma due to the electrical asymmetry effect (EAE). The EAE is established via the simultaneous application o...

The effect of the shape of the applied voltage waveform on the energy efficiency of reactive species generation is investigated in an atmospheric pressure RF microplasma jet operated in a He/O2 mixture (99.5%/0.5%) based on a one-dimensional hybrid fluid-kinetic simulation method. Using a tailored waveform synthesized from four consecutive harmonic...

The PlasmaKristall-4 experiment on the International Space Station allows for the study of the 3-dimensional interaction between plasma and dust particles. Previous simulations of the PK-4 environment have discovered fast moving ionization waves in the dc discharge[1]. These ionization waves vary the plasma parameters by up to an order of magnitude...

Neutral radicals generated by electron impact dissociation of the background gas play important roles in etching and deposition processes in low pressure capacitively coupled plasmas (CCPs). The rate and energy efficiency of producing a given radical depend on the space- and time-dependent electron energy distribution function (EEDF) in the plasma,...

Based on experiments and simulations, various plasma parameters are found to undergo a hysteresis as a function of the driving voltage amplitude in capacitively coupled CF4 discharges. Phase Resolved Optical Emission Spectroscopy reveals that the discharge operates in a hybrid combination of the drift-ambipolar and α-mode at low voltage. In this mo...

The electron power absorption mechanisms in electronegative capacitively coupled plasmas in CF4 are investigated using particle-in-cell/Monte Carlo collisions simulations at a pressure of p= 60 Pa, a driving frequency of f= 13.56 MHz for voltage amplitudes in the interval of ϕ0= 100 − 300 V, where pronounced self-organized density variations, i.e....

A dual-frequency ( $2f$ ) capacitively coupled rf argon plasma has been investigated using a passively compensated Langmuir probe (LP). The discharge is driven by two different excitation frequencies (13.56 and $27.12~\mathrm{MHz}$ ) simultaneously with a variable phase angle $\theta$ between them, utilizing the electrical asymmetry effect (EA...

Phase Resolved Optical Emission Spectroscopy (PROES) measurements combined with 1d3v Particle-in-Cell/Monte Carlo Collision (PIC/MCC) simulations are performed to investigate the excitation dynamics in low-pressure capacitively coupled plasmas (CCPs) in argon-oxygen mixtures. The system used for this study is a geometrically symmetric CCP reactor o...

A spatially two dimensional fluid-MC hybrid (fluid-kinetic) simulation method is developed and applied to the COST reference microplasma jet operated in helium with an oxygen admixture of 0.5\%, excited by a single frequency voltage waveform with $f=13.56$~MHz and $V_{\rm rms}=275$~V. The simulation approach is based on a fluid model augmented by a...

The Electrical Asymmetry Effect (EAE) provides control of the mean ion energy at the electrodes of multi-frequency capacitively coupled radio frequency plasmas (CCP) by tuning the DC self bias via adjusting the relative phase(s) between the consecutive driving harmonics. Depending on the electron power absorption mode, this phase control affects th...

Phase Resolved Optical Emission Spectroscopy (PROES) measurements combined with 1d3v Particle-in-Cell/Monte Carlo Collision (PIC/MCC) simulations are performed to investigate the excitation dynamics in low-pressure capacitively coupled plasmas (CCPs) in argon-oxygen mixtures. The system used for this study is a geometrically symmetric CCP reactor o...

The kinetics of excited atoms in a low-pressure argon capacitively coupled plasma source are investigated by an extended Particle-in-Cell / Monte Carlo Collisions simulation code coupled with a Diffusion-Reaction-Radiation code which considers a large number of excited states of Ar atoms. The spatial density distribution of Ar atoms in the 1s$_5$ s...

With the increasing demands towards large area plasma etching and deposition, the radial uniformity of capacitively coupled plasmas (CCPs) becomes one of the key factors that determine process performance in industrial applications. However, there is a variety of parasitic effects, e.g. electromagnetic and electrostatic edge effects, that typically...

We present scanning drift tube measurements of electron swarm transport coefficients in CO as a function of the reduced electric field E/N at room temperature under time-of-flight (TOF) conditions. The measurements are compared to modeling results and other available experimental data on swarm transport over the broad range of E/N from 2 Td to 1603...

Capacitively coupled plasmas are routinely used in an increasing number of technological applications, where a precise control of the flux and energy distribution of ions impacting boundary surfaces is required. In the presence of dielectric wafers and targets the accumulation of charges on these surfaces can significantly alter the time evolution...

Phase resolved optical emission spectroscopy (PROES) measurements combined with 1d3v particle-in-cell/Monte Carlo collisions (PIC/MCC) simulations are used to study the electron power absorption and excitation/ionization dynamics in capacitively coupled plasmas (CCPs) in mixtures of neon and oxygen gases. The study is performed for a geometrically...

A low-pressure capacitively coupled radiofrequency (RF) helium discharge with a structured electrode is investigated experimentally and via kinetic simulations. In the experiment, Phase Resolved Optical Emission Spectroscopy (PROES) provides information about the excitation dynamics by high energy electrons, with high spatial and nanosecond tempora...

The magnetized Drift-Ambipolar ("m-DA") electron power absorption mode and a sequence of structural transitions, including the formation of an electropositive core where the electron density is much higher than the negative ion density, are identified in a magnetized capacitive RF plasma of a strongly electronegative gas, CF4. The m-DA mode is caus...

Particle-in-cell with Monte Carlo collisions (PIC/MCC) is a fully kinetic, particle based numerical simulation method with increasing popularity in the field of low temperature gas discharge physics. Already in its simplest form (electrostatic, one-dimensional geometry, and explicit time integration), it can properly describe a wide variety of comp...

Capacitively coupled plasmas are routinely used in an increasing number of technological applications, where a precise control of the quantity and the shape of the energy distribution of ion fluxes impacting boundary surfaces is required. Often times, narrow peaks at controllable energies are required, e.g. to improve selectivity in plasma etching,...

Phase Resolved Optical Emission Spectroscopy (PROES) measurements combined with 1d3v Particle-in-Cell/Monte Carlo Collisions (PIC/MCC) simulations are used to study the electron power absorption and excitation/ionization dynamics in capacitively coupled plasmas (CCPs) in mixtures of neon and oxygen gases. The study is performed for a geometrically...

The physical characteristics of an argon discharge excited by a single-frequency harmonic waveform in the low-intermediate pressure regime (5-250 Pa) are investigated using Particle-in-Cell/Monte Carlo Collisions simulations. It is found that, when the pressure is increased, a non-negligible bulk electric field develops due to the presence of a ``p...

Self-organization of dust grains into stable filamentary dust structures (or “chains”) largely depends on dynamic interactions between individual charged dust grains and complex electric potential arising from the distribution of charges within a local plasma environment. Recent studies have shown that the positive column of the gas discharge plasm...

The electron power absorption dynamics and plasma uniformity in low pressure capacitively coupled RF discharges with structured electrodes are investigated by graphics processing unit-based 2d3v particle-in-cell/Monte Carlo simulations in argon gas. In the presence of planar electrodes, the plasma is radially nonuniform due to strong electron densi...

An interesting aspect of complex plasma is its ability to self-organize into a variety of structural configurations and undergo transitions between these states. A striking phenomenon is the isotropic-to-string transition observed in electrorheological complex plasma under the influence of a symmetric ion wake field. Such transitions have been inve...

Recent studies have shown that the positive column of the gas discharge plasma in the Plasmakristall-4 (PK-4) experiment onboard the International Space Station (ISS) supports the presence of fast-moving ionization waves, which lead to variations of plasma parameters, such as the axial electric field, and the electron and ion number densities, temp...

External magnetic fields impose diverse effects on low-temperature plasmas. We study these in a low-pressure capacitively coupled radio frequency plasma in argon via self-consistent kinetic simulations. The primary effect of the transversal magnetic field, that manifests itself in the trapping of electrons at lower excitation frequencies and, thus,...

Particle based simulations are indispensable tools for numerical studies of charged particle swarms and low-temperature plasma sources. The main advantage of such approaches is that they do not require any assumptions regarding the shape of the particle velocity/energy distribution function (VDF/EDF), but provide these basic quantities of kinetic t...

Particle-in-cell with Monte Carlo collisions (PIC/MCC) is a fully kinetic, particle based numerical simulation method with increasing popularity in the field of low temperature gas discharge physics. Already in its simplest form (electrostatic, one-dimensional geometry, explicit time integration) it can properly describe a wide variety of complex,...

Understanding the spatio-temporal dynamics of charged particles in low pressure radio frequency capacitively coupled plasmas (CCP) is the basis for knowledge based process development in these plasma sources. Due to the importance of kinetic non-local effects the particle in cell/Monte Carlo collision (PIC/MCC) simulation became the primary modelin...

An interesting aspect of complex plasma is its ability to self-organize into a variety of structural configurations and undergo transitions between these states. A striking phenomenon is the isotropic-to-string transition observed in electrorheological complex plasma under the influence of a symmetric ion wakefield. Such transitions have been inves...

Using data from equilibrium molecular dynamics computer simulations we have built up a catalog of response functions for the Coulomb one-component plasma over a wide range of Γ coupling values, including the strongly coupled Γ>1 liquid regime. We focus on the domain of negative compressibility (Γ>3), where the proper response displays an acausal be...

The effects of the simultaneous presence of two different types of plasma asymmetry, viz, geometric and electrical, on low-pressure capacitively coupled argon discharges are studied by 2D3V graphics-processing-unit-based particle-in-cell/Monte Carlo simulations. The geometric asymmetry originates from the different powered vs grounded electrode sur...

Low pressure single- or dual-frequency capacitively coupled radio frequency (RF) plasmas are frequently used for high-aspect ratio (HAR) dielectric etching due to their capability to generate vertical ion bombardment of the wafer at high energies. Electrons typically reach the wafer at low energies and with a wide angular distribution during the lo...

Using data from equilibrium Molecular Dynamics computer simulations we have built up a catalogue of response functions for the Coulomb one-component plasma (OCP) over a wide range of $\Gamma$ coupling values, including the strongly coupled $\Gamma > 1$ liquid regime. We focus on the domain of negative compressibility ($\Gamma>3$), where causality a...

For the self-consistent description of various plasma sources operated in the low-pressure (nonlocal, kinetic) regime, the Particle-In-Cell simulation approach, combined with the Monte Carlo treatment of collision processes (PIC/MCC), has become an important tool during the past decades. PIC/MCC simulation codes have been developed and maintained b...

We present a combined experimental and numerical investigation of the plasma properties in an asymmetric capacitively coupled radio frequency plasma source using argon discharge. Besides driving the system in the conventional way, which results in a high negative self-bias voltage VDC due to the asymmetric configuration, we also connect a ‘quarter-...

In this paper, we describe an efficient, massively parallel GPU implementation strategy for speeding up one-dimensional electrostatic plasma simulations based on the Particle-in-Cell method with Monte-Carlo collisions. Relying on the Roofline performance model, we identify performance-critical points of the program and provide optimised solutions....

Observations made in dusty plasma experiments suggest that an ensemble of electrically charged solid particles, confined in an elongated trap, develops structural inhomogeneities. With narrowing the trap the particles tend to form layers oriented parallel with the trap walls. In this work we present theoretical and numerical results on the structur...

The PK-4 system is a micro-gravity dusty plasma experiment currently in operation on-board the International Space Station. The experiment utilizes a long DC discharge in neon or argon gases. We apply our 2D particle-in-cell with Monte Carlo collisions discharge simulation to compute local plasma parameters that serve as input data for future dust...

Two experimental apparatuses used to obtain electron transport coefficients in gases are compared based on measurements in CO 2 over a wide range of E / N -values. The operation principles of the two experimental systems as well as their data acquisition methods are different. One operates under the time of flight (TOF) principle, where the transpo...

The influence of a uniform magnetic field parallel to the electrodes on radio frequency capacitively coupled oxygen discharges driven at 13.56 MHz at a pressure of 100 mTorr is investigated by one-dimensional particle-in-cell/Monte Carlo collision (1D PIC/MCC) simulations. Increasing the magnetic field from 0 to 200 G is found to result in a drasti...

The equilibrium structure and the dispersion relations of collective excitations in trilayer Yukawa systems in the strongly coupled liquid regime are examined. The equilibrium correlations reveal a variety of structures in the liquid phase, reminiscent of the corresponding structures in the solid phase. At small layer separation substitutional diso...

In high aspect ratio (HAR) dielectric plasma etching, dual-frequency capacitively coupled radio-frequency plasmas operated at low pressures of 1 Pa or less are used. Such plasma sources are often driven by a voltage waveform that includes a low-frequency component in the range of hundreds of kHz with a voltage amplitude of 10 kV and more to generat...

The equilibrium structure and the dispersion relations of collective excitations in trilayer Yukawa systems in the strongly coupled liquid regime are examined. The equilibrium correlations reveal a variety of structures in the liquid phase, reminiscent of the corresponding structures in the solid phase. At small layer separation substitutional diso...

The spatio-temporal ionization and excitation dynamics in low-pressure radiofrequency (RF) discharges operated in neon are studied and a detailed comparison of experimental and kinetic simulation results is provided for a wide parameter regime. Phase resolved optical emission spectroscopy (PROES) measurements and 1d3v particle-in-cell/Monte Carlo c...

This work presents swarm parameters of electrons (the bulk drift velocity, the bulk longitudinal component of the diffusion tensor, and the effective ionization frequency) in C2Hn, with n = 2, 4, and 6, measured in a scanning drift tube apparatus under time-of-flight conditions over a wide range of the reduced electric field, 1 Td ≤ E/N ≤ 1790 Td (...

We investigate via molecular dynamics simulations the propagation of solitons in a two‐dimensional many‐body system characterized by Yukawa interaction potential. The solitons are created in an equilibrated system by the application of electric field pulses. Such pulses generate pairs of solitons, which are characterized by a positive and negative...

Spatially resolved tunable diode-laser absorption measurements of the absolute densities of He-I (23S1) metastables in a micro atmospheric pressure plasma jet operated in He/N2 and driven by 'peaks'- and 'valleys'-type tailored voltage waveforms are presented. The measurements are performed at different nitrogen admixture concentrations and peak-to...

A many-body system of charged particles interacting via a pairwise Yukawa potential, the so-called Yukawa one-component plasma (YOCP), is a good approximation for a variety of physical systems. Such systems are completely characterized by two parameters: the screening parameter, κ, and the nominal coupling strength, Γ. It is well known that the col...

Two-dimensional dusty plasmas can be realized experimentally and are examples of a classical many body system with a screened Coulomb interaction. After discussing experimental approaches, we present the basics of molecular dynamics simulations of dusty plasmas. A web-based platform is developed that allows users to perform molecular dynamics simul...

This work presents swarm parameters of electrons (the bulk drift velocity, the bulk longitudinal component of the diffusion tensor, and the effective ionization frequency) in C$_2$H$_n$, with $n =$ 2, 4 and 6, measured in a scanning drift tube apparatus under time-of-flight conditions over a wide range of the reduced electric field, 1 Td $\leq\,E/N...

We investigate via Molecular Dynamics simulations the propagation of solitons in a two-dimensional many-body system characterized by Yukawa interaction potential. The solitons are created in an equilibrated system by the application of electric field pulses. Such pulses generate pairs of solitons, which are characterized by a positive and negative...

A many-body system of charged particles interacting via a pairwise Yukawa potential, the so-called Yukawa One Component Plasma (YOCP) is a good approximation for a variety of physical systems. Such systems are completely characterized by two parameters; the screening parameter, $\kappa$, and the nominal coupling strength, $\Gamma$. It is well known...

Atmospheric pressure capacitively coupled radio frequency discharges operated in He/N2 mixtures and driven by tailored voltage waveforms are investigated experimentally using a COST microplasma reference jet and by means of kinetic simulations as a function of the reactive gas admixture and the number of consecutive harmonics used to drive the plas...

We investigate the spatially and temporally resolved electron kinetics in a homogeneous electric field in argon gas, in the vicinity of an emitting boundary. This (transient) region, where the electron swarm exhibits non-equilibrium character with energy gain and loss processes taking place at separate positions (in space and time), is monitored ex...

In this paper, we studied the structure and dynamics for a trilayer Yukawa crystal. We firstly studied the optimal lattice structure by comparing lattice interaction energy from different lattice distribution, after that, we did the collective mode calculation and analyzed its eigenvectors, if the lattice structure is stable, all the eigenvalues of...

We investigate the spatially and temporally resolved electron kinetics in a homogeneous electric field in argon gas, in the vicinity of an emitting boundary. This (transient) region, where the electron swarm exhibits non-equilibrium character with energy gain and loss processes taking place at separate positions (in space and time), is monitored ex...

The self-diffusion phenomenon in a two-dimensional dusty plasma at extremely strong (effective) magnetic fields is studied experimentally and by means of molecular dynamics simulations. In the experiment the high magnetic field is introduced by rotating the particle cloud and observing the particle trajectories in a corotating frame, which allows r...

Single frequency, geometrically symmetric Radio-Frequency (RF) driven atmospheric pressure plasmas exhibit temporally and spatially symmetric patterns of electron heating, and consequently, charged particle densities and fluxes. Using a combination of phase-resolved optical emission spectroscopy and kinetic plasma simulations, we demonstrate that t...

The electron power absorption dynamics in radio frequency driven micro atmospheric pressure capacitive plasma jets are studied based on experimental phase resolved optical emission spectroscopy and the computational particle in cell simulations with Monte Carlo treatment of collisions. The jet is operated at 13.56 MHz in He with different admixture...

The self-diffusion phenomenon in a two-dimensional dusty plasma at extremely strong (effective) magnetic fields is studied experimentally and by means of molecular dynamics simulations. In the experiment the high magnetic field is introduced by rotating the particle cloud and observing the particle trajectories in a co-rotating frame, which allows...

This special Issue focuses on the field of dusty plasmas or also referred to as complex plasmas. Most of the papers were presented at the 8th International Conference on the Physics of Dusty Plasmas (8 ICPDP, Fig. 1 ), which was hosted by Charles University and held in Prague, Czech Republic, on May 20–25, 2017. We would like to join the continuou...

We discuss the origin of uncertainties in the results of numerical simulations of low-temperature plasma sources, focusing on capacitively coupled plasmas. These sources can be operated in various gases/gas mixtures, over a wide domain of excitation frequency, voltage, and gas pressure. At low pressures, the non-equilibrium character of the charged...

The direct experimental determination of the 3-point static structure function S⁽³⁾(k1, k2, k0) of a 2-dimensional dusty plasma liquid is presented. The measurements are complemented by molecular dynamics simulations of the system, using parameters (dust charge, plasma frequency, coupling and screening coefficients), which are derived from the expe...

Dynamic characteristics of strongly coupled classical one-component Coulomb and Yukawa plasmas are obtained within the nonperturbative model-free moment approach without any data input from simulations so that the dynamic structure factor (DSF) satisfies the first three nonvanishing sum rules automatically. The DSF, dispersion, decay, sound speed,...

We present a very simple and sensitive method to measure the sputtering rate of solid materials in stationary low-pressure gas discharges. The method is based on the balance of the centrifugal force and the confinement electric force acting on a single electrically charged dust particle in a rotating environment. We demonstrate the use and sensitiv...

A magnetic field was recently shown to enhance field-parallel heat conduction in a strongly correlated plasma whereas cross-field conduction is reduced. Here we show that in such plasmas, the magnetic field has the additional effect of inhibiting the isotropization process between field-parallel and cross-field temperature components thus leading t...

A magnetic field was recently shown to enhance field-parallel heat conduction in a strongly correlated plasma whereas cross-field conduction is reduced. Here we show that in such plasmas, the magnetic field has the additional effect of inhibiting the isotropization process between field-parallel and cross-field temperature components thus leading t...

In a two-dimensional (2D) dusty plasma composed of superparamagnetic, charged dust grains and immersed in an external magnetic field B, the grains interact via both Yukawa and magnetic dipole-dipole potentials. Because the grains' magnetic dipole moments are induced by B, the dipole moments all lie along B. When B is tilted with respect to the norm...

The influence of an external homogeneous magnetic field on the quasilocalization of the particles—characterized quantitatively by cage correlation functions—in strongly coupled three-dimensional Yukawa systems is investigated via molecular dynamics computer simulations over a wide domain of the system parameters (coupling and screening strengths, a...

Low pressure capacitive radio frequency (RF) plasmas are often described by equivalent circuit models based on fluid approaches that predict the self-excitation of resonances, e.g., high frequency oscillations of the total current in asymmetric discharges, but do not provide a kinetic interpretation of these effects. In fact, they leave important q...

Using the “rotodust” experimental setup [1] at the Hypervelocity Impacts and Dusty Plasmas Lab (HIDPL) of the Center for Astrophysics, Space Physics, and Engineering Research (CASPER) at Baylor University we have realized effective magnetization of single layer dusty plasma systems in the strongly coupled state up to thousands of Teslas of magnetic...

In low-pressure capacitive discharges the radio-frequency modulated plasma sheaths generate a number of highly energetic beam electrons traversing the discharge gap. These electrons are important for sustaining the plasma via ionization. In this work, we investigate the dynamics of these electron beams as well as their effect on the plasma by means...

In many-body systems the convolution approximation states that the 3-point static structure function, $S^{(3)}(\textbf{k}_{1},\textbf{k}_{2})$, can approximately be "factorized" in terms of the 2-point counterpart, $S^{(2)}(\textbf{k}_{1})$. We investigate the validity of this approximation in 3-dimensional strongly-coupled Yukawa liquids: the fact...

We propose a method to generate a single peak at a distinct energy in the ion flux-energy distribution function (IDF) at the electrode surfaces in capacitively coupled plasmas. The technique is based on the tailoring of the driving voltage waveform, i.e. adjusting the phases and amplitudes of the applied harmonics, to optimize the accumulation of i...

Experiments and particle-based kinetic simulations were performed to obtain the equilibrium levitation height of dust particles in plane parallel electrode discharges in low pressure argon gas, established by combined RF and DC excitation. The computed values were compared to experimental data. The good overall agreement of the simulation results a...