Empirical Transport Scaling
Energy lifetimes in present experiments are set by particle/flux diffusion and radiation.
Empirical diffusion
- ?? = 17.5xs1/2n1/2(1021m-3)rs2(m) msec
- ?p = 31xsn1/2(1021m-3)rs2(m) msec
Uniform resistivity model calculation
- ?? = rs2/16(??/?o) ? ??/?o = 3.6/xs1/ 2n1/2(1021m-3) m2/s
- ?p = xsrs2/16D? ? D? = (?/2)??/?o = 2.0/n1/2(1021m-3) m2/s
FRC diffusion coefficients are in the same range as in tokamaks, but the lifetime is short since the plasmas are high beta (low internal flux) and the minor radius, a ~ rs/4 ~ 5 cm is only about 10 ion gyroradii.
The empirical scaling is sufficient for pulsed high density reactors, but the implied degradation at low densities must be improved by about an order of magnitude to allow for small steady-state reactors.
- There is some evidence for improvement in low density Japanese experiments.