In view of the recent remarkable advancement of computer technology and simulation software, simulation studies are one of the most powerful academic tools for establishment of quantitative space physics and modelling of our space environment. The complex nature encountered in space plasma physics has motivated considerable development in computer simulations, which have played an essential role in the development of space plasma theory. This report describes research undertaken to understand physical processes involved in plasma waves observed in the magnetospheric plasmas, and associated nonlinear phenomena such as heating, diffusion, and acceleration of particles due to excited waves. The research explains and clarifies the observational data both qualitatively and quantitatively

Nishikawa, Ken-Ichi

English

NASA Technical Reports Server

Particle Simulations in Magnetospheric Plasmas
NAGW-1239
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Ken-Ichi Nishikawa
Department of Physics and Astronomy
The University of Iowa
Iowa City, IA 52242
26 January 1990
Final Technical Report for Period 1 November 1988 - 31 October 1989
[ Distribution Statement ]
Prepared for
NASA Technical Monitor
Space Physics Division
NASA Headquarters
Washington, DC, 20546
NASA Scientific and Technical Information Facility
P. O. Box 8757, Baltimore/Washington International Airport
MD 21240
(NASA-CR-18_23_) PARTICLF SIMULATInNS IN
_AGNETOSPHE_IC PLASMA_ Final Technical
Report v I Nov. 19_8 - 31 Oct. IQdQ (Iowa
U_iv.) 7 p C_CL ?Of G317S
N90-1493_
https://ntrs.nasa.gov/search.jsp?R=19900005618 2020-03-19T23:36:07+00:00Z
Technical Description of Project and Results
Brief Summary
In view of the recent remarkable advancement of computer technology and simulation
software, simulation studies are one of the most powerful academic tools for establishment
of quantitative space physics and modelling of our space environment. The complex nature
encountered in space plasma physics has motivated considerable development in computer
simulations, which have played an essential role in the development of space plasma theory.
This final technical report describe research to understand physical processes involved in
plasma waves observed in the magnetospheric plasmas, and associated nonlinear phenomena
such as heating, diffusion, and acceleration of particles due to excited waves. Our research
have elucidated the observational data both qualitatively and quantitatively. We need further
development of new simulation codes and simulation studies.
1. Simulation Study of a New Mechanism for Excitation of Kinetic Waves in a
Magnetoplasma
Nishikawa et al. [1988b] have investigated the new ion-cyclotron-like waves by a localized
transverse electric field by means of simulation with the assistance of the nonlocal kinetic theory
[Ganguli et al., I985a, b]. The linear theory shows that the growth rates of the kinetic KeNin-
Helmholtz (K-H) modes are strongly reduced with increasing u = kll/ky , and they become
2 2
unstable only when b = kypi < 1 and k_L _ 1, where L is the scale length associated with
the transverse electric field. On the other hand, the new modes have larger frequencies and
become unstable at larger b > 1 and k_L :>> 1 [Ganguli et al., 1988].
Simulation results show that ion-cyclotron-like waves are excited in regions where E × B
drift is localized. Linear growth rates of several modes are obtained from the wave analysis of
the simulation. This linear analysis shows that the (0, 4) mode corresponds to large b, and large
k_L has the maximum growth rate. Clearly, these are not K-H modes. Further, the simulation
results show that density gradients help to enhance the growth rates. This is in contrast to
the established properties of the K-It instability ISatyanarayana et al., 1987]. However, like
the K-H mode, the real frequencies of this instability are approximately proportional to kyV_,
where V_ is the peak value of the E x B drift.
Nonlinear phenomena such as diffusion and coalescence of vortices are investigated. In
the linear stage smaller vortices are generated and larger vortices with the lower frequencies are
dominant in the nonlinear stage. In the nonlinear stage ions diffuse strongly due to large-scale
vortices.
Recently, we have investigated the electrostatic waves driven by the combined effects of
a localized transverse electric field and parallel electron drifts by means of simulation with the
assistance of the nonlocal kinetic theory [Ganguli and Palmadesso, 1988; Ganguli et al., 1989].
2
Wehaveperformeda numberof simulations for this instability [Nishikawa et al., 1989b,
1990a]. Simulation results show that electrostatic waves are excited in the regions where the
E × B drift is localized in the simultaneous presence of parallel electron drifts and transverse
electric fields. Simulations with only parallel electron drifts or transverse electric fields show
that no instability grows out of the thermal noise. The simulation with both the parallel
electron drift and the transverse electric field shows the growing waves out of the thermal
noise. The Doppler shift due to the E x B drift can lower the phase velocity of waves along the
magnetic field. Then this makes wave-particle resonance possible for smaller Vd°, which leads
to this instability.
2. Simulation of Electron Cyclotron Harmonic Waves by AMPTE Lithium Release
On September 11 and again on September 20, 1984, a cloud of lithium gas was released
in the solar wind upstream of the Earth's bow shock as a part of the AMPTE (Active Magneto-
spheric Particle Tracer Explorers) program. Numerous effects were observed in the immediate
vicinity of the release including: (1) the creation of a dense rapidly expanding cloud of ionized
lithium, (2) the formation of a diamagnetic cavity, and (3) the occurrence of an intense shock-
like burst of electrostatic noise in the region upstream from the cavity. A detailed analysis of
the shock-like electrostatic noise and investigation of the origin of this noise is presented by
Gurnett et al. [1986a]. Also comparisons are made with a similar type of noise observed in the
Earth's bow shock [Gurnett et al., 1986a].
A simulation study of the electrostatic noise in the cloud of released lithium ions has
been performed [Nishikawa et al., 1990b]. Using a two-dimensional electrostatic code, we have
simulated plasmas consisting of four components as observed. In this study, electrons and ions
are magnetized, unlike the theory [Gurnett et al., 1986a; Ma et al., 1987; Omidi et al., 1988].
However, the gyro-radii of ions are much larger than the size of the simulation system as well
as the scale size of the ion cloud. Since the gyro-radii of hot electrons are smaller than the
size of the simulation system, electron cyclotron waves and upper hybrid waves are included.
This is important because electrostatic electron cyclotron harmonic (ECtt) waves are observed
by the AMPTE-IRM plasma wave experiment following a lithium release in the solar wind
[Roeder et al., 1987].
The simulations show that electron cyclotron harmonic waves are excited by the solar
wind protons and electrons [Nishikawa et al., 1990b]. The spectra of perturbations of electro-
static potential exhibit electron cyclotron harmonic waves.
The overall frequency range is obtained by observing the electric fields at some points in
the simulation region. Power spectra of the electric fields exhibit electron cyclotron frequency
and higher harmonics which is simular to the spectrum obtained by the satellite.
The possible mechanisms of generation of electron cyclotron harmonic waves are dis-
cussed in the previous work [Roeder et al., 1987]. In this simulation study, the possible energy
sources of the instability are included automatically. The relative velocities among different
species become the energy source of instabilities. The relative velocity between solar wind elec-
trons andlithium ionswouldbe the possibleenergysourcefor the excitationof ECH waves.
The fact that the instability canbe excitedwithout new-borncold electronssupportsthis
mechanism.
Accordingto Figure 1 by Gurnett et al. [1986a], the higher frequency ranges of waves
look very similar in both cases with _ti _ np_ and _ti << n'-pr. In this study, we found that ECH
waves are excited also in the case of _li = np_. The satellite data show that ECH waves can be
observed only in some range of lithium ion density (0.03 - 0.18 cm -3) associated with lithium
drift energy [Roeder et al., 1987]. The observations show that in the case of nli _" n--pr ECH
waves are not found. The simulation results show that in the same case ofn/i = n-'pr ECH waves
are excited. This discrepancy may be explained by the setting of simulation geometry due to
the two-dimensional code. If the simulation plane is set nearly parallel to the magnetic fields
(Boy/Bo < 1), the angle between the magnetic fields and the drift velocity of hot electrons and
protons becomes very small. Then, in the case of nil = n'-pr, the parallel drift of solar wind
protons and electrons may excite ion acoustic waves more dominantly than ECH waves, which
is not included in this study [Gurnett et al., 1986a; Ma et al., 1987; Omidi et al., 1988].
Related to the previous discussion, we performed the simulation with the parameter
Boy/Bo = 0.371 keeping other parameters the same as the first case. In this case, the drift
velocity of protons and hot electrons along the y-direction becomes 13.9vp_t and the angle
between the magnetic field and the drift velocity is 49.2 °. The case of the lithium release on
September 11, 1984 has much smaller angle between the magnetic field and the drift velocity
(in which the drift velocity perpendicular to the magnetic field is very small). The geometry
of this simulation has a qualitative resemblance with that of the observation on September 11,
1984. The simulation results show that ECH waves are not excited. Therefore, the excitation
of ECH waves depends on the angle between the magnetic field and the drift velocity (the
value of the perpendicular drift velocity).
3. Beam Instability in the Foreshock
As an application of the simulation method used in the proposed research (Broadband
electrostatic noise), the beam instability in the foreshock has been investigated. Electrons
backstreaming into the Earth's foreshock generate waves near the plasma frequency by the
beam instability [Etcheto and Faucheux, 1984; Fuselier et al., 1985; Lacombe et al., 1985;
Garnett, 1985]. Two versions of the beam instability exist: the 'reactive' version [Buneman,
1963] in which narrowband waves grow by bunching the electrons in space, and the 'kinetic'
version in which broadband growth occurs by a maser mechanism [Cairns, 1887a, b; Dum, 1989,
and references therein]. Recently, Cairns [1987b] has suggested that (1) the backstreaming
electrons have steep-sided "cutoff" distributions which are initially unstable to the reactive
instability, (2) the back-reaction to the wave growth causes the instability to pass into its
kinetic phase, and (3) the kinetic instability saturates by quasilinear relaxation.
Cairns and Nishikawa [1989] have performed two-dimensional simulations of the reactive
instability for Maxwellian beams and cutoff distributions. The results of the simulations are
consistent with suggestions (1) and (2) above. In addition, we have demonstrated that the
4
reactiveinstability is a bunchinginstability, andthe reactiveinstability saturatesand passes
overinto the kinetic phaseby particle trapping. Wefoundthat the kinetic growth occurring
after saturationof thereactiveinstability ispresumablydueto thespatiallylocalizedgradients
in y- vii phase space. Both simulation results and numerical solutions of the dispersion equation
indicate that the center frequency of the intense narrowband waves near the foreshock boundary
may be between 0.9wpe and 0.98wp_, rather than being above wpe as previously believed.
4. 3-D Particle simulation of Whistler Mode Driven by the Spacelab 2 Electron
Beam
During the Spacelab 2 mission while an electron beam was being ejected from the shuttle,
the Plasma Diagnostics Package (PDP) detected a clear funnel-shaped emission that is believed
to be caused by whistler-mode emission from the electron beam [Gurnett et al., 1986b; Farrell
et al., 1988, 1989]. In order to understand the mechanism of this emission, the simulations have
been performed using a three-dimensional magnetostatic code for low-fl plasmas [Okuda et al.,
1979] in which the beam electrons are initially located in the column [Nishikawa et al., 1989a,
and references therein]. In order to simulate the continuous electron ejection from the shuttle,
the simulations were also performed with the recycling of the beam electrons. The beam
electrons excite whistler waves and lower hybrid waves. The brief fluid theory based on the
magnetostatic code was checked with the simulation results. The propagating whistler mode
was identified with the theory. The simulation results show that the quasi-perpendicularly
(the angle between the magnetic field and the wavenumber is larger than 50 °) propagating
whistler waves have larger amplitude whose real frequencies are smaller than the local electron
cyclotron frequency. This fact is consistent with the fact that the funnel-shaped emission is
observed below the electron cyclotron frequency away from the beam electrons [Omura and
Matsumoto, 1988a, b]. The beam electrons initially in the column diffuse radially as well
as slow down due to the E × B caused by the excited waves. The acceleration of the beam
electrons also takes place due to the excited whistler waves.
In order to compare with the PDP data, the local magnetic fields Bz,v and the perturbed
electric fields Ev,, are diagnosed at the several points in the simulation system. The results show
that the waves are radially excited by the beam electrons localized in the center of the system.
The wave spectra of the electric fields Ev,, diagnosed at z = 31A,, y = 16Ae, and z = 17A, show
the several kinds of waves generated by the beam electrons. The analysis shows that the lower
hybrid waves and whistler waves are excited. The frequency range of these spectra extends
from ¢opi to beyond wp, which is in qualitative agreement with the PDP data. As the PDP
data show, the intense electrostatic narrowband emission around the electron plasma frequency
has been observed dominantly in the spectra of the electric field (Ez) with and without the
recycling of the beam electrons. This wave is identified as the parallel (quasi parallel) whistler
wave. This simulation result is in good agreement with the PDP data [Gurnett et al., 1986b].
At the present the maximum memory is 6 Mwords on CRAY XMP/48 at National Center
for Supercomputing Applications at July, 1988. It was increased up to 100 Mwords on CRAY-2
in 1989; now we will be able to use a larger system such as Lx x Ly × Lz = 128 x 128 x 256A 3.
Simulationswith this sizewill providemorerealisticcomparisonswith the observeddata.
List of Publications Prepared under NASA Support (as of January 26, 1990)
Nishikawa, K.-I., L. A. Frank, T. E. Eastman, and C. Y. Huang,
Simulation of electrostatic turbulence in the plasma sheet boundary layer with electron
currents and ion beams, in Magnetotail Physics, edited by A. T. Y. Lui Johns Hopkins
University Press, p. 313, 1987.
Nishikawa, K.-I., L. A. Frank, and C. Y. Huang,
Simulation of electrostatic turbulence in the plasma sheet boundary layer with electron
currents and bean-shaped ion beams J. Geophys. Res., 93, 5929, 1988a.
Nishikawa, K.-I., G. Ganguli, Y. C. Lee, and P. Palmadesso,
Simulation of ion-cyclotron-like modes in a magnetoplasma with a transverse inhomoge-
neous electric field, Phys. Fluids, 31, 1568, 1988b.
Nishikawa, K.-I., L. A. Frank, and C. Y. Huang,
Three-dimensional simulation of whistler mode excited by the Spacelab 2 electron beam,
J. Geophys. Res., 94, 6855, 1989a.
Cairns, I. H. and K.-I. Nishikawa,
Simulations relevant to the beam instability in the foreshock plasma, J. Geophys. Res.,
94, 79, 1989.
Nishikawa, K.-I., G. Ganguli, Y. C. Lee, and P. Palmadesso,
Simulation of electrostatic ion instabilities in the presence of parallel currents and trans-
verse electric fields, Physics of Space Plasma (1989), SPI Conference Proceedings and
Reprints Series, Number 8, T. Chang, G. B. Crew, and J. R. Jasperse, eds., Scientific
Publishers, Inc., Cambride, MA, 1989b, p. 405; also in Proceedings of an International
School and Workshop on Plasma Astrophysics, ESA SP-285 (Vol. 1), p. 385, ESA,
Paris, France, 1989b.
Nishikawa, K-I., G. Ganguli, Y. C. Lee, and P. J. Palmadesso,
Simulation of electrostatic turbulence due to sheared flow parallel and transverse to the
magnetic field, J. Geophys. Res., 95, 1029, 1990a.
Nishikawa, K.-I., J. L. Roeder, and H. C. Koons
Simulation of electron cyclotron harmonic waves by AMPTE lithium release, to be re-
submitted to J. Geophys. Res. 1990b
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Particle simulations in magnetospheric plasmas

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