/* Copyright (C) 2003 Valerij Pipin <pip@iszf.irk.ru>
 *
 * This program is free software; you can redistribute it and/or
 * modify it under the terms of the GNU General Public License as
 * published by the Free Software Foundation; either version 2 of
 * the License, or (at your option) any later version.
 *
 * This program is distributed in the hope that it will be
 * useful, but WITHOUT ANY WARRANTY; without even the implied
 * warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR
 * PURPOSE.  See the GNU General Public License for more details.
 *
 * Examine magnetic field lines embedded in moving plasma
 *
*/

if get('itensor,'version)=false then load(itensor);
("Examine magnetic field lines embedded in moving plasma")$
("introduce the 2-form describing the magnetic field")$
decsym(B,2,0,[anti(all)],[]);
("Due to infinite conductivity the electric field is expressed as")$
E1:ishow(B([i1,i2])|v)$
("But we can also express it through the vector potential")$
E2:ishow(expand(2*extdiff(A([i1]),i2)|v))$
("and put this result in the following equation:")$
EQ1:ishow(dt*B([i1,i2])=extdiff(E2,i1))$
("Now compute the Lie-derivative of B")$
EQ2:ishow('liediff(v,B([i2,i1]))=liediff(v,extdiff(A([i1]),i2)))$
("and sum up the LHS and RHS")$
ishow(lhs(EQ1)+lhs(EQ2)=rename(expand(rhs(EQ1)+rhs(EQ2))))$

/* End of demo -- comment line needed by MAXIMA to resume demo menu */