XXXVII international conference on plasma physics and CF, February 8 – 12, 2010, Zvenigorod.
SOLITONS IN TWO-FLUID MHD WITH NON-ZERO ELECTRON INERTIA
M.B. Gavrikov, V.V. Savelyev, A.A. Tayurskiy
Keldysh Institute of Applied Mathematics RAS, Moscow, Russia, [email protected]
The results of analytical and numerical investigation of solitary waves on the basis of two-fluid
MHD with non-zero electron inertia for cold plasma are presented in the report. Nonlinear waves
with linear polarization of a magnetic and electric fields are considered.
U x  
H2 
 U x

0 ,
  U x2  z   0
t
x
t
x 
8 
(1)
2
c 2 mi me  E y U x H z cmi me   H z 
1 H z E y

 0, E y 


U x

c t
x
4 e 2 x 2
с
4 e 2 x 
x 
Non-zero mass of electron and respectively nonlocal Ohm’s law are the reason for wave dispersion.
This effect is especially important for short waves then  ck  pe   1 . A main difference of the
2
present work is the using of the "exact" equations (1), instead of the modeling equations. The phase
velocity of solitary wave a has to satisfy with condition VA  a  2 VA ( VA  H 0 / 40 ) and its
amplitude is proportional to phase velocity - H S  2( a / VA  1) H 0 . It is numerically shown, that
solitary waves are solitons really, i.e. their interaction is similar to interaction of colliding particles.
On figure it is shown as an example the process of «collision» of two solitons with equal amplitudes
and opposite signs of phase velocity.
1