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 mo

ving 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 colli

sions?• The issue has puzzled scientists more tha

n five decades.• Heating of plasma in the downstream is o

bserved 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 eit

her laminar or turbulent.• The reason is that the solar wind con

ditions vary from time to time.• Three parameters control the bow sh

ock 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

0 240

0z p A

pi

k k c k vk vk 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 casesLow-Mach number and parallel shocks

• Most difficult caseLow-Mach number and low beta s

hocks

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 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 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

1ˆcossv

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

1ˆcossv

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 hi

gh-speed beam• Moreover, the beam electrons poss

ess 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.