A method for obtaining three-dimensional computational equilibrium of non-neutral plasmas using WARP

Gomberoff, K.; Wurtele, J. S.; Friedman, A.; Grote, D.P.; Vay, Jean‐Luc

doi:10.1016/j.jcp.2007.02.029

Cited by 14 publications

(9 citation statements)

References 21 publications

(44 reference statements)

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“…We use a technique to relax the simulated plasma to an equilibrium in a uniform field that was developed 13 for anti-hydrogen traps. We then ramp the mirror field and find numerical agreement with a basic theory that describes the equilibrium distribution in the mirror geometry.…”

Section: Discussionmentioning

confidence: 99%

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Simulation studies of non-neutral plasma equilibria in an electrostatic trap with a magnetic mirror

et al. 2007

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The equilibrium of an infinitely long, strongly magnetized, non-neutral plasma confined in a Penning-Malmberg trap with an additional mirror coil has been solved analytically [J. Fajans, Phys. Plasmas 10, 1209 (2003)] and shown to exhibit unusual features. Particles not only reflect near the mirror in the low field region, but also may be weakly trapped in part of in the high field region.The plasma satisfies a Boltzmann distribution along field lines; however, the density and the potential vary along field lines. Some other simplifying assumptions were employed in order to analytically characterize the equilibrium; for example the interface region between the low and high field regions was not considered. The earlier results are confirmed in the present study, where two-dimensional particle-in-cell simulations are performed with the Warp code in a more realistic configuration with an arbitrary (but physical) density profile, realistic trap geometry and magnetic field. A range of temperatures and radial plasma sizes are considered. Particle tracking is used to identify populations of trapped and untrapped particles. The present study also shows that it is possible to obtain local equilibria of non-neutral plasmas using a collisionless PIC code, by a scheme that uses the inherent numerical collisionality as a proxy for physical collisions.2

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Section: Discussionmentioning

confidence: 99%

“…[12][13] This work was conducted at UC Berkeley as part of the ALPHA 8 collaboration. Future ALPHA experiments will use a mirror field.…”

Section: Introductionmentioning

confidence: 99%

Simulation studies of non-neutral plasma equilibria in an electrostatic trap with a magnetic mirror

et al. 2007

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“…By solving Poisson's equation, the electrostatic potential is then calculated from the charge density. Currently artificial numerical collisions are included in the WARP simulations to approximate real collisions [20]. The rotational symmetry of the microtrap allows the use of the two dimensional version of WARP.…”

Section: Particle-in-cell (Pic) Warp Simulationmentioning

confidence: 99%

“…In this stage the rotating frequency and the temperature is dependent of r while these values become constant on very long time scales (few seconds) in the case of global equilibrium with the help of shear forces and radial heat transport [14]. As the plasma attains equilibrium in which there is no transport across the magnetic field, the root mean square of axial velocity (RMS V z ) should reach to a constant value, although it has been shown [20] that there could be some oscillations in the this value when a plasma nears the equilibrium in a PM trap. The evolution of RMS V z is plotted in Fig.…”

Section: Toward the Equilibriummentioning

confidence: 99%

Simulation studies of the behavior of positrons in a microtrap with long aspect ratio

et al. 2014

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The charged particles storage capacity of microtraps (micro-Penning-Malmberg traps) with large length to radius aspect ratios and radii of the order of tens of microns was explored. Simulation studies of the motions of charged particles were conducted with particle-in-cell WARP code and the Charged Particle Optics (CPO) program. The new design of the trap consisted of an array of microtraps with substantially lower end electrodes potential than conventional Penning-Malmberg traps, which makes this trap quite portable. It was computationally shown that each microtrap with 50 µm radius stored positrons with a density (1.6 × 10 11 cm −3 ) even higher than that in conventional Penning-Malmberg traps (≈ 10 11 cm −3 ) while the confinement voltage was only 10 V . It was presented in this work how to evaluate and lower the numerical noise by controlling the modeling parameters so the simulated plasma can evolve toward computational equilibrium. The local equilibrium distribution, where longitudinal force balance is satisfied along each magnetic field line, was attained in time scales of the simulation for plasmas initialized with a uniform density and Boltzmann energy distribution. The charge clouds developed the expected radial soft edge density distribution and rigid rotation evolved to some extent. To reach global equilibrium (i.e. rigid rotation) is to be reached in longer runs. The plasma confinement time and its thermalization were independent of the length. The length-dependency, reported in experiments, is due to the fabrication and field errors. Computationally, more than one hundred million positrons were trapped in one microtrap with 50 µm radius and 10 cm length immersed in a 7 T uniform, axial magnetic field, and the density scaled as r −2 down to 3 µm. Larger densities were trapped with higher barrier potentials.

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“…Generally, these simulations reproduce with great accuracy the evolution of the electron density measured in the experiments, when condition (1) is satisfied and viscous/collisional effects may be neglected. Limitations to the 2D approximation have nonetheless been pointed out [27], and inherently three-dimensional cases have been also investigated [28,29].…”

Section: Introductionmentioning

confidence: 99%

Coherent structures and turbulence evolution in magnetized non-neutral plasmas

Romé

Chen²,

Maero

2018

AIP Conference Proceedings

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The evolution of turbulence of a magnetized pure electron plasma confined in a Penning-Malmberg trap is investigated by means of a two-dimensional particle-in-cell numerical code. The transverse plasma dynamics is studied both in the case of free evolution and under the influence of non-axisymmetric, multipolar radio-frequency drives applied on the circular conducting boundary. In the latter case the radio-frequency fields are chosen in the frequency range of the low-order azimuthal (diocotron) modes of the plasma in order to investigate their effect on the insurgence of azimuthal instabilities and the formation and evolution of coherent structures, possibly preventing the relaxation to a fully-developed turbulent state. Different initial density distributions (rings and spirals) are considered, so that evolutions characterized by different levels of turbulence and intermittency are obtained. The time evolution of integral and spectral quantities of interest are computed using a multiresolution analysis based on a wavelet decomposition of density maps. Qualitative features of turbulent relaxation are found to be similar in conditions of both free and forced evolution, but the analysis allows one to highlight fine details of the flow beyond the self-similarity turbulence properties, so that the influence of the initial conditions and the effect of the external forcing can be distinguished. In particular, the presence of small inhomogeneities in the initial density configuration turns out to lead to quite different final states, especially in the presence of competing unstable diocotron modes characterized by similar growth rates.

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A method for obtaining three-dimensional computational equilibrium of non-neutral plasmas using WARP

Cited by 14 publications

References 21 publications

Simulation studies of non-neutral plasma equilibria in an electrostatic trap with a magnetic mirror

Simulation studies of non-neutral plasma equilibria in an electrostatic trap with a magnetic mirror

Simulation studies of the behavior of positrons in a microtrap with long aspect ratio

Coherent structures and turbulence evolution in magnetized non-neutral plasmas

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