Shaped Velocity Distribution Research Articles

Sub-grid modeling of pitch-angle diffusion for ion-scale waves in hybrid-Vlasov simulations with Cartesian velocity space

Numerical simulations have grown to play a central role in modern sciences over the years. The ever-improving technology of supercomputers has made large and precise models available. However, this accuracy is often limited by the cost of computational resources. Lowering the simulation's spatial resolution in order to conserve resources can lead to key processes being unresolved. We have shown in a previous study how insufficient spatial resolution of the proton cyclotron instability leads to a misrepresentation of ion dynamics in hybrid-Vlasov simulations. This leads to larger than expected temperature anisotropy and loss-cone shaped velocity distribution functions. In this study, we present a sub-grid numerical model to introduce pitch-angle diffusion in a 3D Cartesian velocity space, at a spatial resolution where the relevant wave–particle interactions were previously not correctly resolved. We show that the method is successfully able to isotropize loss-cone shaped velocity distribution functions, and that this method could be applied to simulations in order to save computational resources and still correctly model wave–particle interactions.

Excitation of Alfvén eigenmodes by fusion-born alpha-particles in D-3He plasmas on JET

Alfvén eigenmode (AE) instabilities driven by alpha-particles have been observed in D-3He fusion experiments on the Joint European Torus (JET) with the ITER-like wall. For the efficient generation of fusion alpha-particles from D-3He fusion reaction, the three-ion radio frequency scenario was used to accelerate the neutral beam injection 100 keV deuterons to higher energies in the core of mixed D-3He plasmas at high concentrations of 3He. A large variety of fast-ion driven magnetohydrodynamic modes were observed, including the elliptical Alfvén eigenmodes (EAEs) with mode numbers n = −1 and axisymmetric modes with n = 0 in the frequency range of EAEs. The simultaneous observation of these modes indicates the presence of rather strong alpha-particle population in the plasma with a ‘bump-on-tail’ shaped velocity distribution. Linear stability analysis and Fokker–Planck calculations support the observations. Experimental evidence of the AEs excitation by fusion-born alpha-particles in the D-3He plasma is provided by neutron and gamma-ray diagnostics as well as fast-ion loss measurements. We discuss an experimental proposal for the planned full-scale D-T plasma experiments on JET based on the physics insights gained from these experiments.

Numerical simulation of unconstrained cyclotron resonant maser emission

When a mainly rectilinear electron beam is subject to significant magnetic compression, conservation of magnetic moment results in the formation of a horseshoe shaped velocity distribution. It has been shown that such a distribution is unstable to cyclotron emission and may be responsible for the generation of Auroral Kilometric Radiation (AKR) -an intense rf emission sourced at high altitudes in the terrestrial auroral magnetosphere. PiC code simulations have been undertaken to investigate the dynamics of the cyclotron emission process in the absence of cavity boundaries with particular consideration of the spatial growth rate, spectral output and rf conversion efficiency. Computations reveal that a well-defined cyclotron emission process occurs albeit with a low spatial growth rate compared to waveguide bounded simulations. The rf output is near perpendicular to the electron beam with a slight backward-wave character reflected in the spectral output with a well defined peak at 2.68GHz, just below the relativistic electron cyclotron frequency. The corresponding rf conversion efficiency of 1.1% is comparable to waveguide bounded simulations and consistent with the predictions of kinetic theory that suggest efficient, spectrally well defined radiation emission can be obtained from an electron horseshoe distribution in the absence of radiation boundaries.

Publisher's Note: “Numerical investigation of auroral cyclotron maser processes” [Phys. Plasmas 17, 056501 (2010)

When a mainly rectilinear electron beam is subject to significant magnetic compression, conservation of magnetic moment results in the formation of a horseshoe shaped velocity distribution. It has been shown that such a distribution is unstable to cyclotron emission and may be responsible for the generation of auroral kilometric radiation—an intense rf emission sourced at high altitudes in the terrestrial auroral magnetosphere. Particle-in-cell code simulations have been undertaken to investigate the dynamics of the cyclotron emission process in the absence of cavity boundaries with particular consideration of the spatial growth rate, spectral output and rf conversion efficiency. Computations reveal that a well-defined cyclotron emission process occurs albeit with a low spatial growth rate compared with waveguide bounded simulations. The rf output is near perpendicular to the electron beam with a slight backward-wave character reflected in the spectral output with a well defined peak at 2.68 GHz, just below the relativistic electron cyclotron frequency. The corresponding rf conversion efficiency of 1.1% is comparable to waveguide bounded simulations and consistent with the predictions of kinetic theory that suggest efficient, spectrally well defined emission can be obtained from an electron horseshoe distribution in the absence of radiation boundaries. © 2010 American Institute of Physics.

Numerical investigation of auroral cyclotron maser processes

When a mainly rectilinear electron beam is subject to significant magnetic compression, conservation of magnetic moment results in the formation of a horseshoe shaped velocity distribution. It has been shown that such a distribution is unstable to cyclotron emission and may be responsible for the generation of auroral kilometric radiation—an intense rf emission sourced at high altitudes in the terrestrial auroral magnetosphere. Particle-in-cell code simulations have been undertaken to investigate the dynamics of the cyclotron emission process in the absence of cavity boundaries with particular consideration of the spatial growth rate, spectral output and rf conversion efficiency. Computations reveal that a well-defined cyclotron emission process occurs albeit with a low spatial growth rate compared with waveguide bounded simulations. The rf output is near perpendicular to the electron beam with a slight backward-wave character reflected in the spectral output with a well defined peak at 2.68 GHz, just below the relativistic electron cyclotron frequency. The corresponding rf conversion efficiency of 1.1% is comparable to waveguide bounded simulations and consistent with the predictions of kinetic theory that suggest efficient, spectrally well defined emission can be obtained from an electron horseshoe distribution in the absence of radiation boundaries.

Symbolic computation of the phoretic acceleration of convex particles suspended in a non-uniform gas

A package has been developed for calculating analytic expressions for forces and torques onto an arbitrarily shaped convex tracer (aerosol) particle small compared to the mean free path of the surrounding nonequilibrium gas. The package Phoretic allows to compute analytical (and also numerical) expressions for forces and torques stemming from elastic and diffusive scattering processes parameterized by an accommodation coefficient. The method is based on calculating half-sphere integral tensors of arbitrary rank and on integrating forces and torques acting on surface elements. The surrounding gas is completely specified by an arbitrarily shaped velocity distribution function. Accordingly, Phoretic requires two inputs: A particle (surface) geometry and a velocity distribution function. For example, the particle may be a cylinder with flat end caps, and the distribution function the one of Maxwell (isotropic) or Grad (13th moment approximation). The package reproduces analytic results for spheres which were available in the literature, and the ones for other geometries (cylinders, cuboids, ellipsoids) which were, however, only partially available (some works considered only elastic collisions, others temperature, or pressure, or only velocity gradients, etc.). In addition, Phoretic takes into account angular velocities which have been usually neglected and become relevant for non-spherical particles. The package is geared towards the implementation of dynamical equations for aerosol particles suspended in dilute or semidilute gases and as such helps to obtain concentration profiles and mobilities of aerosol particles depending on their shape (distribution) and environmental conditions. Program summary Title of program: Phoretic Catalogue identifier:ADYI_v1_0 Program summary URL: http://cpc.cs.qub.ac.uk/summaries/ADYI_v1_0 Program obtainable from: CPC Program Library, Queen's University of Belfast, N. Ireland Licensing provisions: Persons requesting the program must sign the standard CPC-non-profit use license (see license agreement printed in every issue) Computer for which the program is designed and others on which it has been tested: All platforms with a monitor Operating systems or monitors under which the program has been tested: Linux, Windows XP, Unix, Mac-OS Program language used: Mathematica ®, version 5.2 or later. Phoretic makes use of the DiscreteMath‘Combinatorica’ Mathematica ® package Memory required to execute with typical data: 10 MByte No. of lines in distributed program, including test data, etc.: 22 410 No. of bytes in distributed program, including test data, etc.: 114 657 Distribution format:tar.gz Nature of physical problem: Starting from a non-uniform velocity distribution function of a gas in terms of its moments, i.e. field variables, and field gradients such as temperature, pressure, or velocity field, the problem is to analytically calculate forces and torques acting onto arbitrarily shaped convex tracer (aerosol) particles small in size compared to the mean free path of the gas. The collision process is modeled as a superposition of elastic and diffusive scattering processes (parameterized by 0 ⩽ α ⩽ 1 ). Method of solution: We implemented the solution to this problem in the symbolic programming language Mathematica ®. The program allows to specify an arbitrary shape of the tracer particle and an arbitrary distribution function of the gas and returns symbolic or numerical expressions for forces and torques. The solution requires the calculation of half-sphere and base surface integrals and subsequent symbolic algebraic and tensorial manipulations. Restrictions on the complexity of the problem: Not known. In case the software cannot calculate surface integrals analytically it offers the possibility to proceed with a numerical evaluation of the corresponding terms. Typical running time: Typical running times mostly depend on the shape of the tracer particle. For all examples coming together with the software distribution run times are below 5 minutes on a modern single-processor platform.