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.