Educational Software for the Visualization of Space Plasma Processes
C. T. Russell, G. Le, J. G. Luhmann and B. Littlefield
First Published in Mathematics/Science Education and Technology, 1994 (edited by G. H. Marks), 236, Association for the
Advancement of Computing in Education, Charlottesville, 1994.
The UCLA Space Physics Group has developed educational software composed
of a series of modules to assist students with understanding basic concepts
of space plasmas and charged particle motion. Present modules cover
planetary magnetospheres, charged particle motion, cold plasma waves,
collisionless shock waves and the solar wind. The software is designed
around the principle that students can learn more by doing rather than
by reading or listening. The programs provide a laboratory-like environment
in which the student can control, observe and measure complex behavior.
The interactive graphics environment allows the student to visualize the
results of his or her experimentation and to try different parameters
as desired. The current version of the software runs on UNIX-based
operating systems in an X-windows environment. It has been used in a
classroom setting at both UCLA, UCSD and other places around the world.
Laboratory courses have traditionally been an essential adjunct to classroom instruction in the physical sciences. Many
principles are very abstract until the student can experience the effects of those principles in a hands-on experiment.
Moreover, many students learn better by doing rather than by reading or listening. The laboratory course strongly reinforces
the book learning. In space physics it is difficult to construct a traditional laboratory course because the size and expense
of the apparatus necessary to undertake properly scaled experiments would be prohibitive. Fortunately, computers provide
us with a mechanism to supplement the lecture course in a meaningful way. In order to support the classroom instruction
in space physics at UCLA, we have developed a series of software modules that illustrate various concepts related to space
plasmas. At this writing we know of no similar available software for space physics. These modules provide an experimental
experience with physical processes that cannot be studied in the laboratory. They allow the student to compare theoretical
and model results with "observations" obtained using these modules, and to visualize complex physical processes. They
reinforce the classroom instruction, and develop physical intuition.
Seven modules are presently available. While designed as an adjunct to a lecture course in space physics, some of these
modules would be useful in teaching more basic plasma physics concepts. The magnetospheres module takes the student
through various magnetic field models of the Earth's magnetosphere and compares the dipole fields of each of the magnetized
planets. The particle tracing module allows the student to follow the motion of ions and electrons of varying energy in
magnetic and electric fields of varying geometry. The cold plasma wave module allows the student to examine the behavior
of electromagnetic waves in a cold plasma. The solar wind module illustrates the radial variation of the solar wind and
interplanetary magnetic field, how the solar current sheet affects the structure of the interplanetary magnetic field and how
disturbances propagate through the interplanetary medium. The collisionless shock module allows the student to
calculate how the solar wind plasma and magnetic field vary across a collisionless shock as the parameters of the shock and
the solar wind vary. It also allows the user to calculate and display the
MHD phase and group velocities. The currents module allows
a student to calculate ground level magnetic disturbances due
to magnetospheric current systems and to predict the Dst index from
solar wind conditions.
The ionosphere module allows the student to explore the production of
a simple ionosphere.
These modules will continue to be enhanced and new modules added during
the foreseeable future. The development of software such as this is a
complex and expensive undertaking. The programs described below were
developed beginning in the summer of 1991 with the support of the
National Science Foundation and the National Aeronautics and Space
Administration under the Space Grant Universities Program. In the
following sections we describe the programming environment, and then each
of the existing modules in turn.
The Space Physics Education Software was developed to run on Sun Sparc workstations using C, X Windows and Openlook/Motif.
The Space Physics Education Software can be run "remotely" at our site at UCLA and displayed on any suitable local
machine's display. The only requirement is that the local machine run X-windows. This includes Macintoshes, which run
the Mac-X program. Local copies of the Space Physics Education Software can be made easily as well. Please contact
contact the lead author (ctrussell@igpp.ucla.edu) for information on using the code remotely or on how to obtain a copy of
the code.
Portability was kept in mind during development, so the program can run on different UNIX platforms and X-Window
environments. Currently the software can be run on Sun workstations with either SunOS or Solaris. Other systems
that are supported currently are HPUX, IBM/AIX, SGI, DEC/Ultrix and Solaris x86. Soon DEC/Alpha will be added to
this list. Other vendor platforms as will be added when needed.
The magnetospheres module was designed to introduce students to some of the elementary properties of planetary magnetic
fields. The first exercise introduces the dipole magnetosphere of each of the planets. The student can "fly through" the
magnetic field using the mouse to take measurements at any chosen position. The next exercise allows the student to examine
the properties of the "mirror-dipole" magnetosphere of Chapman and Ferraro, and to see in a simple analytic model how
the magnetosphere is compressed by the solar wind. The next level of complexity is the spherical magnetosphere in which
the equatorial field near the boundary is tripled due to the highly curved spherical magnetopause surface. This can be
compared in the next exercise to Tsyganenko's [1989a] vacuum magnetosphere which is confined inside an elongated ellipse.
With its realistically shaped dayside magnetopause, the field at the nose in this model is compressed by a factor of 2.44 over
the undisturbed dipole field at this distance. The final exercise allows the student to probe Tsyganenko's [1989b] empirical
magnetosphere which is distorted relative to the vacuum magnetosphere because of the implicit presence of internal plasma.
Figure 1 shows a copy of the window displaying this last option, with a train of mouse-selected position points shown on
a "flight" through the magnetotail.
The particle motion module was designed to demonstrate the behavior of single charged particles moving in magnetic fields
of geophysical interest. On entering the module, the user is presented with a menu of field geometries including Uniform,
Harris Sheet, Dipole, Mirror, Gradient, Curvature magnetic geometries and an E B option that includes a uniform electric
field together with a uniform magnetic field. The Harris current sheet is a simple analytic current sheet of finite thickness
which approximates the Earth's plasma sheet [Harris, 1962]. The user can then choose the desired particle mass (and
charge), including H+, He+, He++, O+, H- and "heavy" electrons. The particle can be started anywhere within the box
showing the field geometry in 3 views by the manipulation of slider bars. Slider bars are similarly used to select the initial
velocity vector components. The particle trajectory is then calculated by a standard finite difference algorithm for initial
value problems. The tracing is terminated by use of a "pause" button. The trajectory can then be erased with another button
and restarted as desired or new trajectories can be superposed on the old using different selectable colors.
Figure 2
shows a display for the dipole field option.
As the trajectory is calculated, the display in the upper right-hand corner shows the constantly updated particle energy, the
accumulated time, the first and last pitch angles, and minimum and maximum positions and velocities. These allow the user
to carry out quantitative "experiments" such as verifying the conservation of energy and of adiabatic invariants, determining
how mass and charge affect drift motions, etc. In some options, parameters of the field model can be varied (eg. the Harris
Sheet thickness) so that the user can also obtain a feeling for how field strength, scale sizes of gradients and current sheets,
and other modifications can affect the particle motion. When the particle motion has stopped, the user can measure positions
on the screen with the mouse-driven cursor. These measurements appear on the bottom of the screen.
The solar wind module was created to communicate concepts related to solar wind and interplanetary magnetic field behavior.
On entering this module, the user chooses either Parker Spiral or Heliospheric Current Sheet options. The Parker Spiral
option allows the user to observe how radial motion of solar wind plasma can lead to the spiral interplanetary field geometry
[Parker, 1958]. The user can use the slider bars to observe how the field geometry is affected by varying the solar wind
velocity (or solar rotation rate) in either the equatorial plane or at a user-selected heliolatitude. The garden hose angle and
field strength and components are also displayed as a function of heliocentric distance. Planet locations are indicated on those
displays to give the user a sense of the radial evolution of solar wind properties.
Figure 3 illustrates the screen for the 3-D
Parker spiral choice.
The Heliospheric Current Sheet option allows the user to "design" a heliospheric current sheet shape by combining magnetic
axis tilt with the introduction of a quadrupolar contribution
to the solar dipole magnetic field. The three-dimensional
interplanetary current sheet shape is then computed and displayed at a user-selected perspective. Solar wind velocity can be
varied by use of a slider bar. The displays together illustrate how the "ballerina skirt" model of the heliospheric current sheet
is controlled by the shape of the neutral line at the solar "source surface". The associated Stream Interaction option allows
the user to impose a specific heliomagnetic latitude profile of solar wind velocity. It directs the program to compute an
approximate model [Hakamada and Akasofu, 1982] of the distortion of the equatorial interplanetary magnetic field given that
velocity profile and the shape of a user-specified current sheet at the source surface. Associated model "time series" of solar
wind properties at various heliocentric distances can also be displayed.
The cold plasma waves module was designed to introduce students to electromagnetic waves in a cold plasma [Stix, 1962].
On entering the module, the user is presented with a menu of wave properties: Index of Refraction, Dispersion Relation,
Phase Velocity, Group Velocity, Parallel Group Velocity, Perpendicular Group Velocity, Ellipticity and Wavelength. The
user can then choose to display how a particular wave property varies as a function of either the frequency or the propagation
angle (the angle between the wave vector and the background magnetic field).
Figure 4 shows an example
of a "phase velocity" option screen. Slider bars are provided in the
screen display that allow the user to select the background magnetic
field strength and the plasma density. To view how the wave property varies as
a function of these parameters, the user can select new values by moving the slider bars and pressing the "Draw Graph"
button. Different colors are used to represent different wave modes (left-handed or right-handed). If the "NORMALIZED"
button is chosen, the frequency is normalized by the proton cyclotron frequency, the velocity is normalized by the Alfven
velocity, and the wave vector is normalized by the inverse of the ion inertial length, the velocity of light divided by the ion
plasma frequency in radians per second.
To view how the wave property varies as a function of a variable such as propagation angle, the user can select a frequency
by either clicking the mouse button in the lower-right box or manually typing in the upper-left box, and then pressing the
"Draw Graph" button. The lower-left box displays the results in a polar plot with the background magnetic field in the
vertical direction. The user can also make a single point measurement for any desired frequency, propagation angle and
plasma conditions. The wave properties displayed in the upper-right box correspond to the parameters in the upper-left box.
The Rankine-Hugoniot module was designed to illustrate how the properties of a plasma, such as density, temperature and
magnetic field change across collisionless shocks. The Rankine-Hugoniot conservation relations, which are incorporated
in this module, allow for predictions of the properties of the downstream plasmas to be made based on knowledge of the
strength of the shock and of the upstream conditions [Tidman and Krall, 1971]. In the Graphs section of this module,
illustrated by
Figure 5, the jump in number density, magnetic field strength, temperature, and plasma beta can be calculated
as a function of one of the controlling upstream parameters. One can vary the Mach number that measures the strength
of the shock, the plasma beta that measures the ratio of the thermal to magnetic pressure, the angle between the upstream
field and the shock normal and the polytropic index in the ideal gas low. By selecting None, the user can find discrete values
for the jumps in the plasma quantities for a given set of upstream parameters. The Case Studies section of this module
allows the user to enter dimensional quantities for the plasma, such as velocity, number density, magnetic field strength,
temperature, etc., and obtain the downstream values for these quantities.
The Specularly Reflected Ions/Shock Foot option allows the calculation
of the distance over which an ion would be reflected by the shock before
it was turned around by the IMF. The MHD portion plots the phase and group
velocities as a function of the propagation angle to the field of user
specified input. Case study output is also available.
The currents module was designed to illustrate the magnetic disturbances
of the surface of the Earth caused by magnetospheric currents. The first
part of this module allows the user to introduce a horizontal current
flowing at a variable ionospheric altitude with a variable azimuth,
strength and latitude. Broad current systems are mimicked by introducing
N wires evenly spaced over the latitude band and each carrying 1/N of
the current. The effort of electrical conductivity of the interior of
the Earth is simulated by the introduction of an optional conducting
layer at a viable depth. Figure 6
shows the X Y Z component of the magnetic field on the surface of
the Earch along a meridian chain of stations from 45 degrees to 90 degrees.
The 1 Megampere current flows westward at 60 degrees latitude and 100 km
altitude. Induced currents have been turned off for this calculation.
The second part of this module enables the user to predict the strength
of the ring current and the Dst
index from measurements of the solar wind and interplanetary magnetic
field.
Figure 7 shows the solar
wind velocity, density and Bz GSM component of the IMF together with the
predicted and observed Dst index. The ring current decay time, the
response of the magnetopause current to the solar wind dynamic pressure,
the quiet time ring current and the energy coupling parameter can
all be varied.
The ionosphere module was designed to illustrate the basic processes leading
to the formation of the ionosphere: the absorption of solar radiation and the
electron production by the declining solar radiation as the density of the
atmosphere increases. The user can vary the scale height of the atmosphere and
the solar zenith angle. Altitude profiles of the radiation flux, the
production function and the electron density are then produced.
Figure 8
shows how the radiation flux, the production function and the resulting density
vary with altitude for a simple alpha Chapman layer. Plots can be overlaid
to see the effects of changing scale height and solar zenith angle.
Interactive, menu-driven graphics software is used both as a tool for graduate students in their dissertation research and also
in computer laboratory exercises to introduce students to the physical processes and phenomena in space plasma physics.
These software tools allow immediate access and display of the data and facilitate the application of standard analyses to the
data such as minimum variance analysis, Fourier analysis, and filtering [Russell, 1983].
Modern commercial mathematical packages are now available that facilitate the manipulation of mathematical expressions,
the integration of functions, the solution of differential equations and the display of the results of these manipulations. At
UCLA we have used Maple (Waterloo Maple Software, info @ maplesoft.on.ca) in computer laboratory exercises and find
that students often extend their use of this software beyond the classroom setting.
From our experience at UCLA, interactive menu-driven graphics software is a good way to introduce students to the physical
processes occurring in space plasmas. We have developed modules for magnetospheres, particle motion, cold plasma, solar
wind, and collisionless shocks. These modules need extension and we need more modules to provide a more complete
curriculum. They are now being used in both upper division and graduate
classes at UCLA and elsewhere. The modules have been best received in computer laboratory situations where the instructor is
available to answer questions. Remote dial-in usage has been less successful due principally to interfacing problems with
x window emulators. Graduate students prefer remote dial-in capability because it allows them freedom to arrange their
schedules but such freedom comes at the price of decreased interaction with the instructor.
We welcome other users. We also welcome new ideas for modules and especially we welcome assistance in developing
modules. Nevertheless, despite our success to date, some problems remain. First, developing software is expensive.
Second, since graduate students and outside users want to run software on a variety of platforms portability is critical.
Fortunately, current developments in computer software and operating systems may assist in mitigating, if not completely
solving, these two problems in the coming years.
We wish to acknowledge the help of Marilyn Van Swol in developing an early
version of this program.
We are also grateful to H. Herbert who has helped install and provide access
to this software, to S.M. Petrinec, M.H. Farris, G. Lindsay and J. Newbury
who developed algorithms for the modules, and to all the students who have provided feedback on the use and
functionality of the programs. This work was supported by the National Aeronautics and Space Administration under
research grant NGT-40005 and by the National Science Foundation under research grant USE 91-55988.
Hakamada, K. and S. I. Akasofu, Simulation of three-dimensional solar wind disturbances and resulting geomagnetic storms,
Space Sci. Rev., 31, 3-70, 1982.
Harris, E.G., On a plasma sheet separating regions of oppositely directed magnetic field, Nuovo Cim., 23, 115, 1962.
Parker, E.N., Dynamics of interplanetary gas and magnetic fields, Ap. 5., 128, 664-676, 1958.
Russell, C.T., Interactive analysis of magnetic field data, Adv. Space Res., 2(7), 173-176, 1983.
Stix, T.H., Theory of Plasma Waves, McGraw-Hill, New York 1962.
Tidman, D.A., and N.A. Krall, Shock Waves in Collisionless Plasmas, Interscience, New York, 1971.
Tsyganenko, N.A., A solution of the Chapman-Ferraro problem for an ellipsoidal magnetopause, Planet Space Sci., 37,
1037, 1989a.
Tsyganenko, N.A., A magnetospheric magnetic field model with a warped tail current sheet, Planet Space Sci., 37, 5,
1989b.
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