Electromagnetic Effects Resulted from Explosions - Ultra and Extremely Low Frequency Electromagnetic Fields - page 429

Here T is the plasma temperature measured in energy units, Ze is the charge of
ions, m e is the electron mass, and L is the Coulomb logarithm (Gaussian system of
units)

( ln r D T

Ze 2

Ze 2 ; u „ 1 I

L D (11.4)

ln r D .m e T/ 1=2
„

Ze 2
u „ 1 I

;

where r D D ǚ T= 4n e e 2 1=2 is the Debye shielding radius, n e is the electron
number density, u is the average relative velocity of electrons and ions, and „ is
the Plank constant. Substituting the average charge of ions Z D 2, the initial
temperature T D 1-10 keV and parameter L D 4 into Eqs. ( 11.3 ) and ( 11.4 )we
obtain the value p 4 10 7 -1 10 9 S=m which is close to the conductivity of
metals under normal conditions.
The perturbations of the Earth magnetic field can diffuse in the conducting
plasma according to Eq. ( 7.7 ). Let R be the radius of the underground chamber
filled with the plasma. Then the characteristic time of the diffusion of GMPs inside
the plasma ball can be estimated as follows:

d 0 p R 2 =4: (11.5)

Taking the above value of p and R D 1 m one can find that d 10 8 -10 9 s,
while the characteristic time of the plasma extension is about t p 10-100 ms
depending on the energy of explosion. Since d t p the Earth magnetic field
lines are completely frozen to the conducting plasma, so that the field lines move
together with the plasma. Thus the plasma motion results in the local distortion of
Earth's magnetic field. The equidistant lines of undisturbed magnetic field B 0 are
schematically shown in Fig. 11.5 a while Fig. 11.5 b displays a picture resulted from
expansion of the conducting plasma ball.
Since the “frozen in” magnetic field is a uniform one in the plasma ball, the
conservation of the magnetic field flux can be written as B 0 R 0 D BR 2 whence
it follows that

B D B 0 R 0 =R 2 ; (11.6)

where B is the induction of uniform magnetic field into the ball with current radius
R and R 0 is the initial radius of the ball. The perturbation, ı B , of the magnetic field
in the ball is given by

ı B D B B 0 D 1 R 0 =R 2 B 0 : (11.7)

If the ground conductivity around the plasma ball can be neglected, then the
magnetic perturbations out of the plasma ball is described by the field of the effective
magnetic dipole given by Eq. ( 7.5 ) where one should replace B by ı B . The magnetic
dipole moment M is directed oppositely to the vector B 0 and this absolute value