/**
* prepare method for bringing the velocity in the desired half step
*
* @param p before the update: v(t); after the update: v(t-dt/2)
*/
public void prepare(Particle2D p, Force f, double dt) {
// a(t) = F(v(t), x(t)) / m
p.ax = f.getForceX(p) / p.mass;
p.ay = f.getForceY(p) / p.mass;
// v(t - dt / 2) = v(t) - a(t)*dt / 2
p.vx -= p.ax * dt / 2;
p.vy -= p.ay * dt / 2;
}
/**
* Boris algorithm for implementing the electric and magnetic field. The damping is implemented
* with an linear error O(dt). Warning: the velocity is stored half a time step before of the
* position.
*
* @param p before the update: x(t), v(t-dt/2); after the update: x(t+dt), v(t+dt/2)
*/
public void step(Particle2D p, Force f, double step) {
// remember for complete()
// a(t) = F(v(t), x(t)) / m
p.ax = f.getForceX(p) / p.mass;
p.ay = f.getForceY(p) / p.mass;
double vxminus = p.vx + f.getPositionComponentofForceX(p) * step / (2.0 * p.mass);
double vxplus;
double vxprime;
double vyminus = p.vy + f.getPositionComponentofForceY(p) * step / (2.0 * p.mass);
double vyplus;
double vyprime;
double t_z = p.charge * f.getBz(p) * step / (2.0 * p.mass); // t vector
double s_z = 2 * t_z / (1 + t_z * t_z); // s vector
vxprime = vxminus + vyminus * t_z;
vyprime = vyminus - vxminus * t_z;
vxplus = vxminus + vyprime * s_z;
vyplus = vyminus - vxprime * s_z;
p.vx =
vxplus
+ f.getPositionComponentofForceX(p) * step / (2.0 * p.mass)
+ f.getTangentVelocityComponentOfForceX(p) * step / p.mass;
p.vy =
vyplus
+ f.getPositionComponentofForceY(p) * step / (2.0 * p.mass)
+ f.getTangentVelocityComponentOfForceY(p) * step / p.mass;
p.x += p.vx * step;
p.y += p.vy * step;
}