Enhanced collisional losses from a magnetic mirror using the Lenard–Bernstein collision operator

Collisions are crucial in governing particle and energy transport in plasmas confined in a magnetic mirror trap. Modern gyrokinetic codes model transport in magnetic mirrors, but some use approximate model collision operators. This study focuses on a Pastukhov-style method of images calculation of particle and energy confinement times using a Lenard– Bernstein model collision operator. Prior work on parallel particle and energy balances used a different Fokker–Planck plasma collision operator. The method must be extended in non-trivial ways to study the Lenard–Bernstein operator. To assess the effectiveness of our approach, we compare our results with a modern finite element solver. Our findings reveal that the particle confinement time scales as a exp(a²) using the Lenard–Bernstein operator, in contrast to the more accurate scaling that the Coulomb collision operator would yield, a² exp(a²), where a² is approximately proportional to the ambipolar potential. We propose that codes solving for collisional losses in magnetic mirrors using the Lenard–Bernstein or Dougherty collision operator scale their collision frequency of any electrostatically confined species. This study illuminates the collision operator’s intricate role in the Pastukhov-style method of images calculation of collisional confinement.