Shock Wave Related Plasma Processes

Major Topics Collisionless heating of ions Fast Fermi acceleration Cyclotron-maser instability

Observations of the Bow Shock First observation of the earth’s bow shock was made with IMP-1 satellite around 1960. First theoretical calculation of the bow shock’s stand-off distance was made by an aerodynamicist at Stanford University based on fluid dynamics. The validity of the calculation was questioned.

The Formation of the Bow Shock The solar wind has a flow speed about 5~8 times the Alfven speed. In the solar wind frame the earth is moving supersonically. As a result, a shock wave is formed in front of the earth. This is the bow shock!

The Physics of Collisionless Heating How can a shock wave occur without collisions? The issue has puzzled scientists more than five decades. Heating of plasma in the downstream is observed by satellites but still not fully understood even today.

Classification by Geometrical Condition Perpendicular Shock Parallel Shock

Classification by Upstream Speed Supercritical Shock Subcritical Shock

Classification by Physical Nature Laminar Shock Waves Turbulent Shock Waves

Two Basic Categories of the Shock Waves In general the bow shock may be either laminar or turbulent. The reason is that the solar wind conditions vary from time to time. Three parameters control the bow shock properties: the shock normal angle, the plasma beta, and the Mach number.

Remember: Shock wave in a plasma is not really a discontinuity !

Numerous plasma instabilities are associated with a collisionless shock.

EM Modified Two-Stream Instability Dispersion equation Special case with

Best Known Instabilities Modified two-stream instability Electromagnetic MTS instability Electron cyclotron drift instability Lower-hybrid drift instability Cross-field streaming instability Current-profile instability

Status of Shock Theories Best understood case High-Mach number and perpendicular shocks Least understood cases Low-Mach number and parallel shocks Most difficult case Low-Mach number and low beta shocks

A fast Fermi process A very efficient acceleration process associated with a shock wave. Observation of 10 keV electrons at the bow shock reported in 1979.

A simple description of ISEE observation Generation of 10 keV electron beam at the point of tangency was observed. Solar wind Bow shock Source point

Fermi Acceleration Fermi acceleration of first kind Two mirror approach each other so that the particles in between can collide many times and gain energy after each reflection Fermi acceleration of second kind Magnetic clouds moving in random directions can result in particle acceleration through collisions.

Basic concept of “fast Fermi” process Particle can gain considerable amount of energy in one “collision” with a nearly perpendicular shock wave. In the De Hoffman-Teller frame particles are moving very fast toward the shock wave. Consequently mirror reflection enables particles to gain energy.

De Hoffman-Teller frame (A moving frame in which there is no electric field)

Magnetic field jump at the shock For a nearly perpendicular shock the jump of magnetic field depends on the upstream Mach number. We can define a loss-cone angle For example, if , we obtain .

Energy gain after one mirror reflection Let us consider that an electron has a velocity equal to the solar wind velocity that is . After a mirror reflection it will have a velocity and the corresponding kinetic energy is .

De Hoffman-Teller frame (A moving frame in which there is no electric field)

(continuation) As an example, let us consider a nearly perpendicular shock wave and If the upstream (bulk) velocity is 400 km/s, we find km/s

Remarks The accelerated electrons form a high-speed beam Moreover, the beam electrons possess a loss-cone feature. These electrons may be relevant to the excitation of em waves.

Shock-Wave Induced CMI Fast Fermi process Energetic electrons Cyclotron maser instability

Study of Collisionless Shock Wave In late 1960s through 1970s the topic attracted much interest in fusion research community. In 1980s space physicists began to take strong interest in the study of collisionless shock. Popular method of research is numerical simulation.

Outlooks Still much room for future research Understanding shock wave must rely on plasma physics This topic area is no longer very hot in the U. S. in recent years.