Study of Conduction Cooling Effects in Long Aspect Ratio Penning-Malmberg Micro-Traps

摘要

A first order perturbation with respect to velocity has been employed to findthe frictional damping force imposed on a single moving charge due to aperturbative electric field, inside a long circular cylindrical trap. We findthat the electric field provides a cooling effect, has a tensorial relationshipwith the velocity of the charge. A mathematical expression for the tensor fieldhas been derived and numerically estimated. The corresponding drag forces for acharge moving close to the wall in a cylindrical geometry asymptoticallyapproaches the results for a flat surface geometry calculated in theliterature. Many particle conduction cooling power dissipation is formulatedusing the single particle analysis. Also the cooling rate for a weaklyinteracting ensemble is estimated. It is suggested that a pre-trap section withrelatively high electrical resistivity can be employed to cool down low densityensembles of electrons/positrons before being injected into the trap. For amicro-trap with tens of thousands of micro-tubes, hundreds of thousands ofparticles can be cooled down in each cooling cycle. For example, tens ofparticles per micro-tube in a $5 cm$ long pre-trap section with the resistivityof $0.46 \Omega m$ and the micro-tubes of radius $50 \mu m$ can be cooled downwith the time constant of $106\mu s$.