Energy and flux moments of multi-beam velocity distributions measured during reconnection

One of the key features of magnetic reconnection is the transfer of magnetic energy into particle energy and flux. Yet standard particle energy and flux moments can be misleading if the underlying particle velocity distribution, f(v) is effectively disjoint. For example, the standard energy moment of an f(v) consisting of a pair of cold beams is found to have ("false") thermal energy. In this case a better strategy is to take the standard moment of each beam (which is bulk kinetic rather than thermal) and add to get the system energy. Both ion and electron velocity distributions measured during magnetic reconnection by instruments such as the Fast Plasma Instrument (FPI) on each of the MMS observatories can be effectively disjoint (see Figure). In this presentation we show how non-standard multibeam energy moments have false thermal energy removed.

Standard moments are velocity moments of a measured f(v). Zero and 1st order moments yield overall density, n, and particle flux, nu. 2nd order moments yield a standard RAM pressure tensor, P_RAM= mnuu, and the thermal pressure tensor, P The traces of these tensors give the scalar bulk kinetic and thermal energy densities. Diagonalization of P enables construction of a temperature ellipsoid for f(v). 3rd order moments yield bulk and thermal energy fluxes such as the bulk kinetic energy flux vector Q_bulk and the thermal flux, Q_thermal = Q_enthalpy + Q_{heat flux}.

Such standard moments contain false thermal parts if f(v) is effectively disjoint and can be represented as a sum of N " beams," f₁ + f₂ + .. + f_N

Multibeam moments lack the false thermal energy present in standard moments. The false thermal energy shows up as increased multibeam bulk kinetic energy! An example of a multibeam moment is, the multibeam thermal pressure tensor, which is a sum of the standard pressure moments of each beam: P^MB = P₁ + P₂ + ... + P_N.

In this presentation we calculate multibeam moments for both idealized and measured disjoint electron and ion f(v) and explain the implications for processes such as particle heating and acceleration.