Grant W. Mason

Simulations of electrostatic modes of non-neutral plasmas with small aspect ratio in a Penning trap

The dependence on induced charge, experimental geometry, and temperature of electrostatic modes in very low aspect ratio non‐neutral plasmas in a Penning trap is considered. The modes are of interest as non‐destructive diagnostics of the shape of the plasmas. These investigations include equilibrium calculations of plasma shapes and profiles at finite temperature and particle‐in‐cell simulations of axisymmetric modes. The results of the simulations are compared to the zero‐temperature theory by Dubin [Phys. Rev. Lett. 66, 2076 (1991)] taken to first‐order in the aspect ratio and to experimental measurements by Weimer et al. [Phys. Rev. A 49, 3842 (1994)]. In general, it is concluded that the Dubin theory provides a means to obtain reasonable estimates of plasma parameters, including density, radius, and axial length, for plasmas in the very important regime for which the axial length is comparable to the Debye length. In addition, dependence on induced charge, equilibrium shape, and plasma temperature are identified which can likely be used to improve agreement between theory and experiment.

Simulations of the instability of the m=1 self-shielding diocotron mode in finite-length non-neutral plasmas

The “self-shielding” m=1 diocotron mode in Malmberg–Penning traps has been known for over a decade to be unstable for finite length non-neutral plasmas with hollow density profiles. Early theoretical efforts were unsuccessful in accounting for the exponential growth and/or the magnitude of the growth rate. Recent theoretical work has sought to resolve the discrepancy either as a consequence of the shape of the plasma ends or as a kinetic effect resulting from a modified distribution function as a consequence of the protocol used to form the hollow profiles in experiments. Both of these finite length mechanisms have been investigated in selected test cases using a three-dimensional particle-in-cell code that allows realistic treatment of shape and kinetic effects. A persistent discrepancy of a factor of 2–3 remains between simulation and experimental values of the growth rate. Simulations reported here are more in agreement with theoretical predictions and fail to explain the discrepancy.

Decay of trapped-particle asymmetry modes in non-neutral plasmas in a Malmberg-Penning trap

The mechanism for the strong damping of diocotron-like azimuthal trapped-particle asymmetry modes in a Malmberg–Penning trap is investigated with a detailed three-dimensional particle-in-cell computer simulation. The m=1,kz≠0 modes are created by a voltage squeeze from a mid-detector ring followed by a displacement of trapped particles in opposite directions on either side of the ring. The voltage squeeze creates a population of particles confined to half the trap length (trapped) and a population of particles that move longitudinally along the full length of the cylinder (untrapped). The damping of the modes is found to be the result of radial transport relative to the m=1 mode (charge) center caused by transitions of particles from untrapped-to-trapped states induced by diffusion of the particles in velocity space. The transport is the immediate consequence of a difference in dynamical orbits for trapped and untrapped particles. The random walk in velocity space results in particles repeatedly changing ...

Large amplitude l=1 coherent structures in non‐neutral plasmas confined in a cylindrical trap

The computation of l = 1 coherent structures in non‐neutral plasmas with arbitrary density profiles and for large displacements of the plasma from the symmetry axis of a confining cylindrical trap is described. As the structures are displaced from the axis, they revolve about the symmetry axis with a frequency that typically increases with displacement. The plasma also is distorted into an approximately elliptical shape. The frequency shifts and the eccentricities as a function of displacement, plasma size, and the shape of the density profile are both computed numerically and calculated analytically. The results are shown to be consistent with data of Fine, Driscoll, and Malmberg [Phys. Rev. Lett. 63, 2232 (1989)] which are measured for relatively large, constant‐density (waterbag) plasmas (R/a = 0.38–0.71) and modest off‐axis displacements (D/a<0.3). Here R is the radius of the plasma at half of peak density when centered, D is the off‐axis displacement, and a is the radius of the cylinder.

Numerical Non‐neutral Plasmas

For the past 15 years, or so, a set of computational tools for studying non‐neutral plasmas has been developed at Brigham Young University. These codes, which include equilibrium codes (for both static plasmas and solitons), radial eigenvalue codes, 2‐d eigenvalue codes, and both 2‐d and 3‐d particle‐in‐cell simulation codes, will be discussed, along with their applications to problems of interest to the non‐neutral plasma physics community.

Damping of Trapped‐Particle Asymmetry Modes in Non‐Neutral Plasma Columns

Asymmetry modes (m = 1, kz ≠ 0) are diocotron‐like modes in finite‐length plasma columns in Malmberg‐Penning traps. We have investigated the modes with a detailed 3‐d particle‐in‐cell (PIC) drift‐kinetic computer simulation. Although PIC simulations do not employ realistic collisions, the simulations in this case reproduce many of the salient features of the data. Particle transport associated with the damping is seen not to be a direct collisional effect, but rather a feature of orbital dynamics associated with transitions from trapped‐to‐untrapped or untrapped‐to‐trapped state relative to the inversion plane of the asymmetry. In the simulations we observe a B−1 dependence of the mode frequencies and a B−0.5 dependence of the damping constant for large rigidity. We further observe a steepening of the dependence of the decay constant to B−2 as the rigidity of the plasma falls below about 2.0. We have also used the simulations to investigate the modes at small seed amplitudes and observe linear flattening ...

Simulations of the instability of the m=1 self-shielding diocotron mode in finite-length nonneutral plasmas

The “self-shielding” m=1 diocotron mode in Malmberg-Penning traps has been known for over a decade to be unstable for finite length nonneutral plasmas with hollow density profiles. Early theoretical efforts were unsuccessful in accounting for the exponential growth and/or the magnitude of the growth rate. Recent theoretical work has sought to resolve the discrepancy either as a consequence of the shape of the plasma ends or as a kinetic effect resulting from a modified distribution function as a consequence of the protocol used to form the hollow profiles in experiments. We have investigated both of these finite length mechanisms in selected test cases using a three-dimensional particle-in-cell code that allows realistic treatment of shape and kinetic effects. We find that a persistent discrepancy of a factor of 2–3 remains between simulation and experimental values of the growth rate.

Underground Muon Data Compared to Hadronic Scaling Predictions from 2 To 1000 TeV

The Utah cosmic ray detector has recorded extensive data on underground muons resulting from the early stages of hadronic cascades in the atmosphere. The measured quantities are sensitive to the hadronic interaction characteristics in the 2--1000 TeV range. The charge ratio of muons has been measured and also calculated semi-analytically by assuming scaling and using fits to accelerator data for production of mesons in hadron-nucleus collisions. In addition, a Monte Carlo program which uses the same assumptions has been developed to calculate rates of observation of multiple muons for comparison with the data. It is observed that the data are consistent with the scaling model calculations up to laboratory energies in excess of 1000 TeV. (auth)