Shock Wave Related Plasma Processes

1. Shock Wave Related Plasma Processes

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

3. 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.

4. 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!

5. 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.

6. Classification by Geometrical Condition • Perpendicular Shock • Parallel Shock

8. Classification by Upstream Speed • Supercritical Shock • Subcritical Shock

9. Classification by Physical Nature • Laminar Shock Waves • Turbulent Shock Waves

10. 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.

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

12. Numerous plasma instabilities are associated with a collisionless shock.

14. EM Modified Two-Stream Instability • Dispersion equation • Special case with

15. 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

16. 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

17. 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.

18. 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

19. 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.

20. 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.

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

22. 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 .

23. 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 .

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

25. (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

26. 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.

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

31. 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.

32. 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.