Then plug in the electron gyroradius. That is the width of the cusp loss hole. I only converted to the Debye length for mathematical convenience.kcdodd wrote:I guess I just don't get your math. To start, what is debye length even supposed to mean when talking about a pure electron sheet. That would mean the thickness of your pure electron sheet would *decrease* with higher densities. That makes no sense to me.
lambda_D^2 = (epsilon_0*kT) / (n_e*e^2)
= 4 * ( (m_e*kT) / (e^2B^2) ) * ( B^2 / (2*mu_0*2*n_e*kT) ) * (epsilon_0*mu_0)*kT/m_e
= rho_e^2 * beta^-1 * 4kT/(m_e*c^2)
I used 2*n_e in beta to account for the ions. beta is (said to be) one. With kT~100 keV, the last term is also about 1, so we see that rho_e is at least very nearly equal to lambda_D.