Topics of Discussion


  • A brief introduction

    Perhaps the best way to approach the concept of a shock is to discuss what types of shocks exist in our daily lives. A few sources of shocks you may not have previously considered include the phenomenon of lightning and thunder, and the earthly movements concerned with volcanic eruptions and earthquakes. Shocks on Earth are more often than not collision-dependent shocks. Earthquakes and volcanic eruptions generate shock waves through the Earth's crust- the aftermath of which are visible to the naked eye. Volcanic eruptions genereate shock waves with their masses of fast moving steam, burning gas and solid material, such as ash and rock. Waves propagate beneath the Earth's crust where collisions occur between fluids and gases of different temperatures and densities. The propagation of these waves then sends an impact shockwave through to the Earth's surface. We feel this shock wave in the form of an earthquake. The initial shock of an earthquake or volcanic eruption in itself then propagates more shock waves along the surface of the Earth, which span for hundreds of miles from the initial site if disruption.

    When space is concerned, a more reasonable comparison of an earthly shock to that found in space is seen in the ocurrance of lightning. Electrical energy heats, pressurizes and ionizes the air within the channel, causing molecules to dissociate to nitrogen and oxygen atoms. These high energy particles form a stream of plasma, a good electrical conductor which is the visible lightning chain. The sound wave we hear when it thunders is generated when a shock wave radius increases and then drops in intensity by heating and compressing greater volumes of air. On a smaller scale, sending an electrical charge through a wire will cause the density of the wire to increase at the shock, expand along the wire and eventually break. Solar flares from the sun work in much the same way. Ionized gas locked into magnetic field lines accelerates towards the earth. Compression and heating across the shock wave takes place by magenetic field interactions rather than on the molecular/atomic collisional encounters, hence, collisionless shock. The small percentage of the ionized gas that reaches the Earth's atomosphere affects radio communications with its high electrically charged energy, and creates the natural phenomenon of the aurora borealis.

    The most simple definition of a shock is a reduction of upstream to downstream flow of supersonic material to subsonic. What does this mean?? Basically, a fluid such as plasma, a product of the solar wind is traveling towards the Earth at a very high velocity- higher than the speed of sound. This fast-moving plasma then encounters the Earth's magnetosphere which has a magnetic field that diverts the plasma flow around it, thus preventing it from streaming right into the earth's atmosphere. When the plasma encounters the magnetosphere, interaction between the charged ions of the plasma and the magnetic field of the magnetosphere cause the plasma streams to decrease in velocity. This is the transition of the plasma streams from supersonic upstream to subsonic downstream flow. At this point, the ions contained in the plasma have two options: to flow through the magnetopause toward the Earth, or to be reflected back upstream by the shock, toward the foreshock. Driven at a high velocity by the solar wind, the plasma bunches up and forms ripples, a shock, as it encounters the magnetopshere. Characteristics of the shock include a multiplicity of waves, as well as turbulence and instability. The shock diverts the majority of the plasma ions around the magnetosphere, allowing only a few to pass though, creating such phenomena as the Aurora Borealis.

  • Examples

    An "earthly" example of a shock would be that of a fighter jet. Just like a boat is able to make bow waves in the water, a jet pushes air molecules until they are compressed to the point that they form shock waves. The shock waves form cones at the head and the tail of the plane, and as they spread along the flightpath, a sonic boom is heard. The shock, or sonic boom in air depends on such factors as weight, size and shape of the aircraft, as well as altitude, weather, flight path and atmospheric conditions. Here is a visual sample of a shock wave on the wing of a 747 commercial jet plane.

  • Air versus Space

    Shockwaves in space differ from those in air. For one, shocks in space are considered to be collisionless- that is, the mean free path of the particles is very large, and less prone to collisions/interactions between neighboring particles. Shocks in air, on the other hand, have a smaller mean free path, and collisions between paticles are common. We have an interest in the collisionless shocks for they suggest that magnetic and electric interactions are shock generative and thereby shocks are not wholly dependent on physical collision between ions, electrons and neutral particles.

    Bow Shock

  • Theories of Study

    There have been many approaches to the study of the bow shock, including the Magnetohydrodynanmics (MHD) approach, and the classical Two Fluid Theory treatment of collisionless shock structure. The magnetohydrodymanics/single fluid theory treats the supersonic plasma streams as homogeneous- having the same temperature and density throughout. The two-fluid theory recognizes the difference between the ion and electron inertial responses, their difference in speed, temperature, and density in comparison to one another. The two-fluid theory assumes the following:

    • Plasma dissipation is local and diffuse
    • Microturbulence is the only kinetic effect pertinent to shocks
    • Magnetic field and and viscosity neglected
    • Velocity distribution of ions and electrons is isotropic and Maxwellian
    • No deposition of wave energy ocurrs outside 2 solar radii

    Additionally, the modern shock structure separates the plasma components into different space phase classes according to how they interact with the shock (ie. reflected ions, etc.). Evidently, not all ions are bound to a single fluid of homogeneous density, velocity and temperature. These approaches have been viewed as problematic to some scientists. More recently, it has been noted that the dissipation in particle acceleration and the change in thermal and magnetic presures along the bow shock is determinded, for the mostpart, by ion dynamics. Thus, ions are treated kinetically and electrons are treated as a single, massless, charge-neutralizing fluid in bow shock simulations.

    Different plasma and hydromagnetic waves are uniquely associated with particle distributions characteristic of each region, which further strays from the fluid theory. Evidently, ions and unbound electrons act differently in the presence of a magnetic field, varying in activity, velocity, density and temperature.

  • Quasi-Perpendicular Shocks

    The activity of the bow shock region surrounding the Earth's magnetosphere is largely dependent on the activity and incidence angle of the solar wind and its ion stablities. Shocks commonly take on two forms- quasi-perpendicular and quasi-parallel. In supercritical quasi-perpendicular shocks, the bow shock magnetic fields do not resemble resistive or dispersive shocks, as predicted by the fluid theory. Instead, ion stablities themselves produce turbulence, thereby decelerating the incoming flow of plasma, and regulating the size of the potential jump upstream.

    The incident solar wind particles which are reflected off the bow shock, have a velocity that is perpendicular to the electric field of the solar wind. This causes the reflected particles to gyrate back upstream aroud the field, and then eventually travel back towards the shock. (see the diagram) It should be noted that at low mach numbers, however, very few ions are reflected off the shock. Another characteristic of the Quasi-Perpendicular shock are the structures generated by the dissipation of ion energy to heat, called shocklets. At very high mach numbers, a shock will form a foot, a ramp and a series of undershoots and overshoots. These components all lead to the formation of the shocklet. For a visual demonstration, we suggest you see our page of simulations. At lower mach numbers, the formation of shocklets is actually prevented. Thus, it has been theorized that there exists a critical mach number for below which, ion reflection is minimal or non-existant, and above which, reflection and wave activity is high.

  • Quasi-Parallel Shocks

    Quasi-parallel shocks, on the other hand, are more disorderly than their quasi-perpendicular counterparts. This fact is attributable to generation of active electromagnetic waves which propagate along a wave vector along the upstream magnetic field. Because the group speed of the bow-shock reflected particles is greater than or equal to that of the upstream speed, they are not reflected back towards the shock as are the gyrating particles of the quasi-perpendiculars shock. Upstream waves are more field aligned and thus, more orderly. A notable characteristic of quasi-parallel shock is the pulsation between upstream and downstream values. Shocks are more turbulent with higher incident mach numbers, and more steady with lesser ones. The shock also has a tenedency to reform on a cyclic basis in the quasi-parallel region, causing a great amount of instability.

    Instability is a great characteritic of the quasi-parallel shock. Just WHY are these shocks so unstable?? For the following reasons: Waves convected by the by the supersonic plasma flow collide with the shock itself, and interactions between the shock and the solar wind cause turbulence in the form of greater wave convection. Then, interaction between the solar wind and the ion beams leaked or reflected by the shock leads to the formation of shocklets. The shock interface oscillation between upstream and downstream is itself inherently unstable, and excites large electromagnetic waves which get convected back downstream. Additionally, cool, dense ion beams are reflected by the shock and sent back upstream toward the incident solar wind plasma. Magnetic pulses are generated by the interaction between the ions and solar wind which eventually grow and steepen, forming a new shock. These magnetic pulses thus lead to the excitation of magnetosonic waves (and pulses). As the magnetosonic pulses grow, they resemble a new shock front.

  • Shock-Related Visuals, Links and Observations

  • Diagrams
  • Simulations

    Last modified 08/13/96 by J. Linville

    Please send comments and questions regarding this tutorial to [email protected]