Variational Principle of Hall Magnetohydrodynamics

The Hall current, which is written by a higher order derivative term, appears as a singular perturbation term to the magnetohydrodynamics (MHD) equations. The Hall MHD system has three invariants, the energy, the magnetic (electron) and ion helicities. The ion helicity is known to be “fragile” with respect to the energy norm of the magnetic and flow fields. In a sense of selective dissipation, the ion helicity may dissipate faster than the energy. Therefore a variational principle that gives minimumenergy state under two helicities constraints becomes an ill-posed problem. On the other hand, studying stability of a shear flow system, its non-Hermitian property invalidates the standard normal-mode analysis or energy principle. The Lyapunov stability analysis (Arnold method) is an effective way to that system. In this analysis, convexity (or coerciveness) of a functional, a linear combination of invariants, plays an important role. However the functional of Hall MHD is not a convex form. It is studied how thedifficulties appear in the variational principle of minimum energy state and Lyapunov stability analysis in the Hall MHD system. In both cases the difficulties stem from the fact that the highest order derivative term in the functional is not positive definite.     

Generation of Alfvén wave energy during magnetic reconnection in Hall MHD

The effect of the reconnection rate on the generation of Alfvén wave energy is systematically investigated using Hall magnetohydrodynamics(MHD). It is well known that a decrease in magnetic energy is proportional to the reconnection rate. It is found that an instantaneous increase in Alfvén wave energy in unit Alfvén time is the square dependence on the reconnection rate. The converted Alfvén wave energy is strongly enhanced due to the large increase in the reconnection rate in Hall MHD. For solar-terrestrial plasmas, the maximum converted Alfvén wave energy in unit Alfvén time with the Hall effect can be over 50 times higher than that without the Hall effect during magnetic reconnection.     

加速器磁场测量的霍尔多探头装置

描述了用于加速器磁场测量的霍尔多探头装置,它包括一个具有三只恒温盒(内有58只霍尔片)的测磁长臂,高精度磁场检定系统以及数据自动获取系统。分别叙述了霍尔片的定位、恒温、校准、数据采集、处理等内容。并提出了多探头装置测量中霍尔片稳定性的重要性。给出了在我们条件下的一些具体数据。本装置已应用在兰州重离子研究装置(HIRFL)的建造过程中,实践证明它能有效地高质量地满足加速器磁场测量的要求。     

A Theoretical Study of MHD Power Generation, (I)

This paper deals with an analysis of the current and electric field distributions in the entrance and exit regions of a linear MHD power generator, for the case where the working fluid (gas) exhibits the Hall effect. For simplicity, the following assumptions are adopted:

1. The MHD power generator is of constant-velocity-type.

2. The problem is two dimensional.

3. The electrical conductivity and the Hall parameter of the fluid and the magnetic field are constant and uniform in the region of interest.

4. The seeding material is injected uniformly at the entrance plane.

Solutions are presented in closed form for several values of the Hall parameter, ωπ. They show that the electric potential in the entrance plane assumes an extreme value between the electrodes, and that the length of the “entrance region” is of the same order as the distance between the electrodes. The influence of electric field distortion at the entrance on the current and electric field distributions is negligible beyond this region. The electric field distortion occurs in the exit region also, resulting in “end loss” which is approximately proportional to σ ^eff ωτ.     

Numerical study of the effect of aft-loaded magnetic field on multiple ionizations in Hall thruster

It is assumed that the shift of a strong magnetic field region with a positive gradient from exit plane to outside, namely the transit from a normal loaded magnetic field to an aft-loaded one, enhances the multiple ionization process in the magnetically shielded Hall thruster. To confirm this conjecture, a comparative study is carried out numerically with a particle-in-cell method. The simulation results prove that compared with the normal loaded magnetic field, the application of aft-loaded magnetic field enhances the multiple ionization process. This study further analyzes the ionization characteristics of the transition from low-charged ions to high-charged ions under two magnetic field conditions and the influence of the magnetic strength of aft-loaded magnetic field on the multiple ionization characteristics. The study described herein is useful for understanding the discharge characteristics of Hall thruster with an aft-loaded magnetic field.     

FRC Simulations using the NIMROD Code

The Plasma Science and Innovation Center (PSI-Center) is benchmarking and refining the NIMROD code for simulations of field-reversed configurations (FRCs). The NIMROD code can resolve highly anisotropic heat conduction and viscosity (Sovinec et al., JCP 195:355, 2004). This combined with its ability to include two-fluid effects, allows us to capture more detailed physics than previous calculations. Recent modifications to the radial boundary conditions capture most of the effects of multiple discrete coils found in many FRC experiments. When the tangential electric field on the end boundaries (open field lines) is set to zero and the Hall term is included in the calculation, the open field-line plasma spins up due to end-shorting effects, which in turn couples to the main FRC plasma through shear viscosity. The spin-up rate is found to be sensitive to the open field-line plasma profile. We are also investigating recent observations (Guo et al., Phys. Rev. Lett. 95:175001, 2005] that imply that a small toroidal field could help stabilize the n = 2 rotational instability. We find that a combination of a relatively weak toroidal magnetic field and the inclusion of the Hall term in the calculation can lead to a change in the character of the mode and a dramatic reduction to its growth rate.     

Effect of the Discharge Voltage on the Performance of the Hall Thruster

In this paper,a two-dimensional physical model is established according to the discharging process in the Hall thruster discharge channel using the particle-in-cell method.The influences of discharge voltage on the distributions of potential,ion radial flow,and discharge current are investigated in a fixed magnetic field configuration.It is found that,with the increase of discharge voltage,especially during 250-650 V,the ion radial flow and the collision frequency between ions and the wall are decreased,but the discharge current is increased.The electron temperature saturation is observed between 400-450 V and the maximal value decreases during this region.When the discharge voltage reaches 700 V,the potential distribution in the axis direction expands to the anode significantly,the ionization region becomes close to the anode,and the acceleration region grows longer.Besides,ion radial flow and the collision frequency between ions and the wall are also increased when the discharge voltage exceeds 650 V.     

Investigation of short-channel design on performance optimization effect of Hall thruster with large height–radius ratio

In this study, the neutral gas distribution and steady-state discharge under different discharge channel lengths were studied via numerical simulations. The results show that the channel with a length of 22 mm has the advantage of comprehensive discharge performance. At this time, the magnetic field intensity at the anode surface is 10% of the peak magnetic field intensity. Further analysis shows that the high-gas-density zone moves outward due to the shortening of the channel length, which optimizes the matching between the gas flow field and the magnetic field, and thus increases the ionization rate. The outward movement of the main ionization zone also reduces the ion loss on the wall surface. Thus, the propellant utilization efficiency can reach a maximum of 96.8%. Moreover, the plasma potential in the main ionization zone will decrease with the shortening of the channel. The excessively short-channel will greatly reduce the voltage utilization efficiency. The thrust is reduced to a minimum of 46.1 mN. Meanwhile, because the anode surface is excessively close to the main ionization zone, the discharge reliability is also difficult to guarantee. It was proved that the performance of Hall thrusters can be optimized by shortening the discharge channel appropriately, and the specific design scheme of short-channel of HEP-1350PM was defined, which serves as a reference for the optimization design of Hall thruster with large height–radius ratio. The short-channel design also helps to reduce the thruster axial dimension, further consolidating the advantages of lightweight and large thrust-to-weight ratio of the Hall thruster with large height–radius ratio.     

Heat transfer effects on flow past an impulsively started semi-infinite vertical plate with uniform heat flux

An implicit finite-difference technique is employed to derive a solution to the flow of an incompressible viscous fluid past an impulsively started semi-infinite vertical plate with uniform heat flux. Transient and steady-state velocity and temperature profiles, the local and average skin-friction and the Nusselt number are shown graphically. The velocity profiles at small values of time t are shown to agree with theoretical solution of the flow past an impulsively started infinite vertical plate with uniform heat flux. The effect of different parameters Pr (the Prandtl number) and Gr (the Grashof number) are studied. It is found that the number of time steps to reach steady-state depends strongly on Grashof number.     

Matching characteristics of magnetic field configuration and chamfered channel wall in a magnetically shielded Hall thruster

To date,the selection of the magnetic field line used to match the chamfered inner and outer channel walls in a magnetically shielded Hall thruster has not been quantitatively studied.Hence,an experimental study was conducted on a 1.35 kW magnetically shielded Hall thruster with a xenon propellant.Different magnetic field lines were chosen,and corresponding tangentially matched channel walls were manufactured and utilized.The results demonstrate that high performance and a qualified anti-sputtering effect cannot be achieved simultaneously.When the magnetic field lines that match the chamfered wall have a strength at the channel centerline of less than 12％ of the maximum field strength,the channel wall can be adequately protected from ion sputtering.When the magnetic field lines have a strength ratio of 12％-20％,the thruster performance is high.These findings provide the first significant quantitative design reference for the match between the magnetic field line and chamfered channel wall in magnetically shielded Hall thrusters.     

Effects of Magnetic Field and Ion Velocity on SPT Plasma Sheath Characteristics

The distribution of magnetic field in Hall thruster channel has significant effect on its discharge process and wall plasma sheath characteristics. By creating physical models for the wall sheath region and adopting two-dimensional particle in cell simulation method, this work aims to investigate the effects of magnitude and direction of magnetic field and ion velocity on the plasma sheath characteristics. The simulation results show that magnetic field magnitudes have small impact on the sheath potential and the secondary electron emission coefficient, magnetic azimuth between the magnetic field direction and the channel radial direction is proportional to the absolute value of the sheath potential, but inversely proportional to the secondary electron emission coefficient. With the increase of the ion incident velocity, secondary electron emission coefficient is enhanced, however, electron density number, sheath potential and radial electric field are decreased. When the boundary condition is determined, with an increase of the sinmlation area radial scale, the sheath potential oscillation is aggravated, and the stability of the sheath is reduced.     

Simulations of the Field-Reversed Configuration with the NIMROD Code

The recently formed Plasma Science and Innovation Center (PSI-Center) is refining the NIMROD code to simulate field-reversed configurations (FRCs). The NIMROD code can resolve highly anisotropic heat conduction and viscosity. This, combined with its ability to include two-fluid effects, allows us to capture more detailed physics than previous calculations. Some initial simulations are focused on 2D (n = 0 only) non-linear two-fluid simulations. We present initial validations of a translating FRC and note good conservation of density and magnetic flux. As a validation of the effects of anisotropic thermal conduction, we present a comparison of an FRC with standard thermal transport to one with anisotropic conduction. Two-fluid simulations are shown which produce significant spin-up due to the end-shorting boundary condition. Finally, simulations of the tilt instability are presented, which show that Hall physics significantly retards, but does not eliminate the growth rate.     

Stabilization in the ZaP Flow Z-Pinch

The stabilizing effect of a sheared axial flow is investigated in an axially flowing Z-pinch that is 1 m long with a 1 cm radius. After pinch assembly the plasma is magnetically confined for an extended quiescent period where the magnetic fluctuation levels of the azimuthal modes m = 1, 2, 3 are significantly reduced. Time-resolved Doppler shifts of plasma impurity lines are measured to determine the plasma axial velocity profiles showing a large, but sub-Alfvenic, sheared flow during the quiescent period and low shear profiles during periods of high mode activity. The plasma has a sheared axial flow that exceeds the theoretical threshold for stability during the quiescent period and is lower than the threshold during periods of high mode activity. The sheared flow profile is coincident with a plasma quiescent period where magnetic mode fluctuations are low. The threshold value and plasma lifetime are experimentally adjusted by controlling the plasma density and plasma supply, which is varied by altering the amount of injected neutral gas. Nonlinear simulations of the Z-pinch are performed using Mach2 for a static plasma, a uniform shear, and a shear localized at the pinch radius.     

Study on the characteristics of non-Maxwellian magnetized sheath in Hall thruster acceleration region

The secondary electron emission (SEE) and inclined magnetic field are typical features at the channel wall of the Hall thruster acceleration region (AR), and the characteristics of the magnetized sheath have a significant effect on the radial potential distribution, ion radial acceleration and wall erosion. In this work, the magnetohydrodynamics model is used to study the characteristics of the magnetized sheath with SEE in the AR of Hall thruster. The electrons are assumed to obey non-extensive distribution, the ions and secondary electrons are magnetized. Based on the Sagdeev potential, the modified Bohm criterion is derived, and the influences of the non-extensive parameter and magnetic field on the AR sheath structure and parameters are discussed. Results show that, with the decrease of the parameter q, the high-energy electron leads to an increase of the potential drop in the sheath, and the sheath thickness expands accordingly, the kinetic energy rises when ions reach the wall, which can aggravate the wall erosion. Increasing the magnetic field inclination angle in the AR of the Hall thruster, the Lorenz force along the $x$ direction acting as a resistance decelerating ions becomes larger which can reduce the wall erosion, while the strength of magnetic field in the AR has little effect on Bohm criterion and wall potential. The propellant type also has a certain effect on the values of wall potential, secondary electron number density and sheath thickness.     

Effects of irradiation with gamma and beta rays on semiconductor Hall effect devices

The effects of short duration irradiation with low dose rate gamma and beta rays on the input resistance and the output Hall voltage of InSb, GaAs, Si, and Ge semiconductor Hall effect devices were systemically studied. Both gamma and beta irradiation can cause the input resistance of Hall effect devices to increase linearly with increasing irradiation time, in the absence of a magnetic field. When the devices were placed in a magnetic field, the output Hall voltage and input resistance increased nonlinearly with increasing gamma irradiation time. The effects of both gamma and beta irradiation persisted long after the irradiation itself, and without annealing. The effects from irradiation in Hall effect devices can be mainly ascribed to the degradation of the charge carriers’ transport properties caused by radiation-induced defects. The radiation resistance of the Hall effect devices was estimated by considering changes of the input resistance under the same irradiation conditions. The Ge and Si Hall effect devices demonstrated a better radiation resistance than the InSb and GaAs Hall effect devices due to their large displacement threshold energy.     

Magnetic Field and Inductance Calculations in Theta-Pinch and Z-Pinch Geometries

Two codes have been developed to model solid metal or wire-wound conductors. The calculations are based on the decomposition of the conductors into arrays of thin wires. The first code, EDDY, models cylindrically symmetric conductors with currents in the theta direction. This code accurately models eddy current induction and magnetic diffusion. It was created in order to aid the design of magnetic-field shields in the FRX-L experiment for Magnetized Target Fusion (MTF). EDDY uses fast, accurate elliptic integral subroutines from MATLAB to solve for the time-dependent current flowing through each wire loop and the resultant magnetic field configuration. The second code, INDIV, models arbitrarily shaped conductors with current flow in the z direction. It was designed to model current division in an inductive divider that would inject current into a liner cavity, for magnetic flux and magnetized-plasma compression experiments. An experiment has been performed to test the INDIV code and the inductive division concept. The numerical results compare well with those of the experiment.     

A Theoretical Study of MHD Power Generation, (II)

The electric potential drop near the electrode surfaces in MHD power generators is studied theoretically by considering a simple model, in which the current flows in the direction normal to the electrode surfaces. In order to simplify the situation so as to permit analytic solution, the idea of a “boundary layer” near the electrodes is introduced, and the problem is treated entirely macroscopically, wherein the following assumptions are made:

1. The electrical conductivity is constant.

2. The Hall effect and the induced magnetic field can be neglected.

3. The behavior of the flow in the boundary layer may be described by equations for laminar flow.

4. The temperature variation in the boundary layer perpendicular to the electrode surfaces may be neglected.

The theory predicts that the magnitude of the electric potential drop near the electrode is of the order of 10 V in typical MHD power generators.     

Stabilization in the ZaP Flow Z-Pinch

The ZaP flow Z-pinch experiment at the University of Washington investigates the innovative plasma confinement concept of using sheared flows to stabilize an otherwise unstable configuration. The ZaP experiment generates an axially flowing Z-pinch that is 1 m long with a 1 cm radius with a coaxial accelerator coupled to a pinch assembly chamber. Magnetic probes measure the fluctuation levels of the azimuthal modes m = 1, 2, and 3. After assembly, the plasma is magnetically confined for an extended quiescent period where the mode activity is significantly reduced. Experimental measurements show a sheared flow profile that is coincident with the low magnetic fluctuations during the quiescent period. Recent experimental modifications produce more energetic Z-pinch plasmas that exhibit the same general behavior. The plasma equilibrium is characterized with a suite of diagnostics that measure the plasma density, magnetic field, ion and electron temperatures, in addition to plasma flow. The equilibrium is shown to satisfy radial force balance.     

PSD位置测量系统在波荡器磁场测量中的应用

位置敏感探测器(Position Sensitive Detector,PSD)是一种基于横向光电效应(x和y方向)的光电位置敏感器件,可直接探测到入射光斑的能量中心位置,在波荡器磁测中可用于获得霍尔探头测量过程中的横向位置变化。为了在狭小或封闭空间内实现对波荡器(尤其是真空内波荡器)磁场进行高精度的测量,我们设计并搭建了测试系统,对导轨直线度(x和y方向)进行了测量。实验结果表明,该位置测量系统具有5μm的测量精度,可以满足霍尔探头在波荡器磁测过程中的位置精度要求。