but the Lawson Criteria is stated as an inequality (co-domain), with Temperature appearing only on the rhs. for any given temperature, the Lawson Criteria sill applies, and equates to our familiar 'confinement time' probability function, or an equivalent (poly-)well gradient.TallDave wrote:Hmm, I don't think so. Basically, it's only applicable for a thermal plasma.
If you're not heating/accelerating the plasma with fusion products, it can't apply, and of course you can't directly accelerate with fusion products.In nuclear fusion research, the Lawson criterion, first derived[1] by John D. Lawson in 1955 and published[2] in 1957, is an important general measure of a system that defines the conditions needed for a fusion reactor to reach ignition, that is, that the heating of the plasma by the products of the fusion reactions is sufficient to maintain the temperature of the plasma against all losses without external power input.
Though, you could argue that if you're feeding fusion products through an alpha conversion mechanism or even (D-D/D-T) through a steam turbine to power the electron drive, that might essentially amount to a less direct version of the same thing.
quoting from wiki (http://en.wikipedia.org/wiki/Lawson_cri ... _ne.CF.84E):: (hope my mark-up is readable)::
so, it appears to me, it has still to obtain, for what we want from WB.wikipedia various - including discussion from art carlson! wrote:
...
where σ is the fusion cross section, v is the relative velocity, and { } denotes an average over the Maxwellian velocity distribution at the temperature T.
...
The volume rate of heating by fusion is f times E_ch, the energy of the charged fusion products (the neutrons cannot help to keep the plasma hot).
The Lawson criterion is the requirement that the fusion heating exceed the losses:
f E_ch >= P_loss
iff
1/4 * n_e^2 {sigma*v} E_ch >= (3n_ek_B * T)/tau_E .....note: 1
iff
n_e tau_E > L === 12/E_ch * k_B * T /{sigma * v}
The quantity T/{sigma * v} is a function of temperature with an absolute minimum. Replacing the function with its minimum value provides an absolute lower limit for the product n_e * T_e. This is the Lawson criterion.
For the D-T reaction, the physical value is at least
n_e * tau_E >= 1.5 * 10^20 s/m^3
The minimum of the product occurs near T = 25 keV.
T is only introduced at 'note 1' above. Any other distribution function can replace the pure { Maxwellian } on offer, so long as other physical relations are still satisfied.
i take your point that, some of the terms get converted, but we can easily see how. the dimensions are the same, the end result is the same.