Education   Space Grant Instructional Computing

Educational Software for the Visualization of Space Plasma Processes

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.

Table of Contents

Introduction

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.

Programming Environment

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.

Magnetospheres

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.

Particle Motion

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.

Solar Wind

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.

Cold Plasma Waves

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.

Collisionless Shocks

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.

Currents

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.

Ionosphere

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.

Other Software Used in the UCLA Space Physics Courses

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.

Concluding Remarks

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.

Acknowledgments

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.

References

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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Last updated: December 31, 1999