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

2 2 4 2 2 2 2

0 24

0

0z p A

pi

k k c k vk v

k v

0 0v

2 2 2 2 2 4 2 4/A z p pik v k k c

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.

Bow shockSource point

Solar wind

Fermi Acceleration

• Fermi acceleration of first kindTwo mirror approach each other so that the particles in between can collide many times and gain energy after each reflection

• Fermi acceleration of second kindMagnetic 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)

1B

1 0HT V B

HTV1v

HTV

1v

1 tanHTV v

1ˆcoss

v

v b

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

.

1arcsincm

BB

1 / 0.5mB B / 6c

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

.

1v

1 2 2s s v v v

22 e sm v

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

electric field)

1B

1 0HT V B

HTV1v

HTV

1v

1 tanHTV v

1ˆcoss

v

v b

(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

88

120,000sv

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.