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Chapter 11: Plasma physics 55

The diffusion coefficient D is defined by means of the flux by = nvdiff = Dn. The equationof continuity is tn +(nvdiff) = 0 tn = D2n. One finds that D = 13vv. A rough estimate givesD = Lp/D = L2pc/

2v. For magnetized plasmas v must be replaced with the cyclotron radius. In electrical

fields also holds J = ne E = e(nee + nii) E with = e/mc the mobility of the particles. The Einsteinratio is:

D

=

kT

e

Because a plasma is electrically neutral electrons and ions are strongly coupled and they dont diffuse inde-

pendent. The coefficient of ambipolar diffusion Damb is defined by = i = e = Dambne,i. From thisfollows that

Damb =kTe/e kTi/e

1/e 1/i kTei

e

In an external magnetic field B0 particles will move in spiral orbits with cyclotron radius = mv/eB0and with cyclotron frequency = B0e/m. The helical orbit is perturbed by collisions. A plasma is called

magnetizedifv > e,i. So the electrons are magnetized if

eee

=

mee3ne ln(C)

6

320(kTe)3/2B0

< 1

Magnetization of only the electrons is sufficient to confine the plasma reasonable because they are coupled

to the ions by charge neutrality. In case of magnetic confinement holds: p = J B. Combined with thetwo stationary Maxwell equations for the B-field these form the ideal magneto-hydrodynamic equations. Fora uniform B-field holds: p = nkT = B2/20.

If both magnetic and electric fields are present electrons and ions will move in the same direction. If E =Erer + Ezez and B = Bzez the E B drift results in a velocity u = ( E B )/B2 and the velocity in ther, plane is r(r,,t) = u + (t).

11.3 Elastic collisions

11.3.1 General

The scattering angle of a particle in interaction with another

particle, as shown in the figure at the right is:

= 2b

ra

dr

r21b2

r2

W(r)

E0

Particles with an impact parameter between b and b + db,moving through a ring with d = 2bdb leave the scatteringarea at a solid angle d = 2 sin()d. The differentialcross section is then defined as:

I() =

dd = bsin() b

T

c

dds

M

b

b

ra

For a potential energy W(r) = krn follows: I(, v) v4/n.

For low energies,

O(1 eV), has a Ramsauer minimum. It arises from the interference of matter waves behind

the object. I() for angles 0 < < /4 is larger than the classical value.