Hall Magnetohydrodynamics - A Tutorial

Over the past fifteen years it has become increasingly clear that Hall magnetohydrodynamics plays a crucial role in many space and laboratory plasma processes: magnetic reconnection, sub-Alfenic plasma expansions, and plasma opening switches to name a few. Hall magnetohydrodynamics is important for plasma dynamics on length scales less than the ion inertial scale length but greater than the electron inertial length. On these scales the ion and electron motions are decoupled; the electrons remain frozen to the magnetic field but the ions are not. In this paper we provide a basic overview of Hall magnetodydrodynamics with an emphasis on numerical methods. We also provide several concrete examples of Hall dynamics: whistler waves, Hall drift waves, plasma opening switch dynamics, and three dimensional magnetic reconnection.

[1]  Weber,et al.  Density redistribution in a microsecond-conduction-time plasma opening switch. , 1992, Physical review letters.

[2]  S. Zalesak.  Fully multidimensional flux-corrected transport algorithms for fluids , 1979 .

[3]  Robert A. Meger,et al.  Vacuum inductive store/pulse compression experiments on a high power accelerator using plasma opening switches. Memorandum report , 1983 .

[4]  Michael Hesse,et al.  Geospace Environment Modeling (GEM) magnetic reconnection challenge: Resistive tearing, anisotropic pressure and Hall effects , 2001 .

[5]  A. Fruchtman.  Penetration and expulsion of magnetic fields in plasmas due to the Hall field , 1991 .

[6]  James Drake,et al.  Structure of the dissipation region during collisionless magnetic reconnection , 1998 .

[7]  R. Denton,et al.  The scaling of collisionless, magnetic reconnection for large systems , 1999 .

[8]  James F. Drake,et al.  Alfvénic collisionless magnetic reconnection and the Hall term , 2001 .

[9]  Grun,et al.  Large-Larmor-radius interchange instability. , 1987, Physical review letters.

[10]  Dimonte,et al.  Dynamics of exploding plasmas in a magnetic field. , 1991, Physical review letters.

[11]  P. Bernhardt,et al.  Observations and theory of the AMPTE magnetotail barium releases , 1987 .

[12]  Michael Hesse,et al.  Collisionless magnetic reconnection: Electron processes and transport modeling , 2001 .

[13]  Drake,et al.  Ion-controlled collisionless magnetic reconnection. , 1995, Physical review letters.

[14]  Lyon,et al.  Theory and simulation of the Rayleigh-Taylor instability in the large Larmor radius. , 1987, Physical review letters.

[15]  J. Greenly,et al.  Nonlinear magnetic field transport in opening switch plasmas , 1993 .

[16]  Drake,et al.  Structure of thin current layers: Implications for magnetic reconnection. , 1994, Physical review letters.

[17]  E. Mclean,et al.  Sub-Alfvenic plasma expansion , 1993 .

[18]  Zhiwei Ma,et al.  Hall magnetohydrodynamic reconnection: The Geospace Environment Modeling challenge , 2001 .

[19]  A. Hassam,et al.  Structuring of the Ampte magnetotail barium releases , 1987 .

[20]  Chuvatin,et al.  Experimental observation of a wedge-shaped density shock in a plasma opening switch. , 1995, Physical review letters.

[21]  Antonius Otto,et al.  Geospace Environment Modeling (GEM) magnetic reconnection challenge: MHD and Hall MHD—constant and current dependent resistivity models , 2001 .

[22]  J. Lyon,et al.  A new 3D MHD algorithm: the distribution function method , 1999, Journal of Plasma Physics.

[23]  James F. Drake,et al.  The role of electron dissipation on the rate of collisionless magnetic reconnection , 1998 .

[24]  Michael Hesse,et al.  Geospace Environmental Modeling (GEM) magnetic reconnection challenge , 2001 .

[25]  K. Hain.  The partial donor cell method , 1978 .

[26]  J. Huba,et al.  Hall magnetohydrodynamic modeling of a long‐conduction‐time plasma opening switch , 1994 .

[27]  J. Huba.  Theory and simulation of a high‐frequency magnetic drift wave , 1991 .

[28]  Rudakov,et al.  Two-dimensional fast penetration of a magnetic field into a homogeneous plasma. , 1992, Physical review letters.

[29]  John M. Grossmann,et al.  Characterization of a microsecond-conduction-time plasma opening switch , 1992 .

[30]  J. M. Neri,et al.  Current distribution in a plasma erosion opening switch , 1984 .

[31]  C. Birdsall,et al.  Plasma Physics via Computer Simulation , 2018 .

[32]  J. D. Huba,et al.  Preliminary study of the CRRES magnetospheric barium releases , 1992 .

[33]  P. Pritchett,et al.  Geospace Environment Modeling magnetic reconnection challenge: Simulations with a full particle electromagnetic code , 2001 .