This page is discussed on the largescale electromagnetic particle simulation (J. Comp. Physics, Tanaka, 1993), and magnetic reconnection (Phys. Plasmas, Tanaka, 1995). This was connected to heavy ions in collisionless parallel shocks (J.Geophys.Res., Shimazu, 1996)
Why is a large amount of the solar-eartth energy released in the distant magnetotail ? This energy release is suddenly and typically observed as magnetic reconnection.
There were many theories for the reconnection including from classical Dungey's theory to nuclear-fusion oriented anomalous resistivity. It is noted that Dr. Speicer paid attention as 'hypothesis' of inertia resistivity of thinning the current sheet. Much later by a particle-in-cell simulation, it was clearly shown and proved that 'inertia of ions and electrons' is the key of input and output flows for magnetic reconnection, then resulting in large energy release of earth's magnetotail (Ref.1).
An electromagnetic particle simulation code is utilized for solar and magnetospheric space physics (Ref. 1,4-5).
The difference of the codes is that, for an explicit particle code, it is strictly bound by the Courant condition,
Dx/Dt < c where Dx is the cell length, Dt is the time step, and c is the speed of light.
On the other hand for the implicit particle code, it is free from this condition, that is Dx/Dt > c and is possible
to make research of solar physics environment.
In the implicit case, both electric and magnetic fields are solved by the implicit condition where the low-frequency slightly backward time decentering technique is used. The backward decentering does not affect low frequency phenomena, \omega*Dt << 1 with \omega = c/Dx (JCP, 1993, Ref. 2,3). Magnetic reconnection and the solar wind-earth magnetic field coupling are quite suitable for applying this simulation code.
One utilizes the time decentered scheme in \aimpl=0.6, while the time centered scheme in the explicit code (\aimpl=0.5) is used in other directory of molecular dynamics simulations. Four physical units are, i) time: 1/wpe (c/wpe: electron inertia length), ii) length: c/wpe, iii) mass: electron mass, and iv) charge: electron charge. The program is written in Fortran 2003 and is coded for parallelization by MPI ver.3. The title, major references, and remarks of this simulation code are written in the top of the @mrg37_023A.f03 file. Major subroutines are named /fulmov/, /emfild/, /cfpsol/, which are used in every time step, while /escorr/ and /fulmv2/ are called in 5 time steps interval.
The correction to the longitudinal part of the electric field is made in /escorr/. Although the Poisson equation for the electric field is to be solved only initially, it is actually not true in the Maxwell equation since numerical errors accumulate in time (see Ref. 2,3). Supporting subroutines are /partpc/ and /srimp1/-/srimp4/. Important blocks of these subroutines are explained as comments. Two additional files are necessary, the parameter file param_A23A.h and the configure file rec_3d23A.
By the implicit scheme it is free from the Courant condition, that is, Dx(length)/Dt(time step) >< c, the speed of light. For the backward differential scheme in \aimpl > 0.5, a time step may be Dt~ 1.2/ \wpe in order to dump out plasma oscillations at plasma frequency \omega_e= \wpe - small noises. But, actually Dt*\wce > 10 is required for electron tracking.
Linux: Compilation by mpif90, gfortran or PGI
mpich-4: ./configure --prefix=/opt/mpich-4 >&1 | tee conf.txt
fftw3: ./configure --disable-shared --enable-maintainer-mode --enable-threads --prefix=/opt/fftw3
mpif90 @mrg37-023A.f03 needs the parameter files param_A23A.h and rec_3d23A
$ mpif90 -mcmodel=medium -fast @mrg37-023A.f03 -I/opt/fftw3/include -L/opt/fftw3/lib -lfftw3
Execution by mpiexec (may need some hundreds of processors)
$ mpiexec -n number_of_cpu a.out &
One can enjoy simulations by changing system sizes and boundary conditions. For the present case, an equilibration of the pair of flux bundles separating the poloidal magnetic field (the y-z component) is first tested in three dimensions. Fully kinetic ions and electrons are used, for example, in the rec_3d23A file. Then, let's start looking at a merging of two flux bundles.
In-house graphic subroutines are incorporated in "@mrg37-023A.f03" in order to check the current run in the simulation. Figure 1 in the "EMfield.pdf" PDF plot shows the electric and magnetic fields in the YZ (left) and X (right) components at the early and final times. Two flux bundles at t= 5000/\wpe are seen touched and sqeezed at the y= Ly/2 plane.
Reading papers of this implicit particle simulation code (Ref. 2,3) and applications to magnetospheric space plasmas (Ref. 1,4,5) are highly recommended.
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M. Tanaka, Macro-particle simulations of collisionless magnetic reconnection, Phys.Plasmas, 2, 2920-2930 (1995).
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M. Tanaka, A simulation of low-frequency electromagnetic phenomena in kinetic plasmas of three dimensions, J.Comput. Phys., 107, 124-145 (1993).
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M. Tanaka, Macro-EM particle simulation method and a study of collisionless magnetic reconnection, Comput.Phys.Commun., 87, 117-138 (1995).
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M. Tanaka, Asymmetry and thermal effects due to parallel motion of electrons in collisionless magnetic reconnection, Phys.Plasmas, 3, 4010-4017 (1996).
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H. Shimazu, M. Tanaka, and S. Machida, The behavior of heavy ions in collisionless parallel shocks generated by the solar wind and planetary plasma interactions, J.Geophys.Res., 101, 27565-27571 (1996).