From: jsm@shade.Princeton.EDU (John Scott McCauley Jr.)
Subject: Re: Latest Lawson Numbers?
Originator: news@nimaster
Organization: Princeton University
Date: Tue, 13 Oct 1992 17:51:29 GMT

In article <1992Oct9.210544.10674@ucsu.Colorado.EDU> eliasen@ucsu.Colorado.EDU (ELIASEN  ALAN BRUCE) writes:
>
>I'm writing a terrible paper about nuclear fusion and comparing it
>with nuclear fission.  I was wondering if someone could help me with a couple
>of questions:
[stuff deleted]
>3.  What Lawson numbers are being achieved by fusion researchers?  And, please,
>   for my reference, could somebody refresh me on the break-even and burn
>   points at the relevant temperatures? Units, too, please?  My subscription to
>   that old LaRoucheite rag "Fusion" has long since expired.  :) 
>

There are two major categories of Lawson numbers, the 'Lawson Tripple Product'
(n tau T_i) and Q, a ratio of fusion heat out versus heat in.

The 'tripple product' is the product of the peak ion density, an energy
``confinement'' time, and the peak ion temperature. Typical high values from
JET (shot 26087) are a density of n=2.9E19 m^-3, tau = 1.2 s, and T_i of about
20 keV, with a tripple product of 9.0E20 m^-3 keV s.

You need to look at a Lawson diagram of n tau vs T_i to interpret these
parameters -- even an old copy of Fusion might have one. Usually, the higher
the number the better. However, the ``breakeven'' curve has a minima near
20 keV so you actaully start doing worse if you exceed 20 keV. I think
for breakeven at 20 keV,  n tau approx 3E19 m^-3 s and ignition about
4E20 m^-3 s.

The other number, Q, is unitless. Unfortunately, there are many ``types''
of Q. JET and TFTR uses different accounting methods. From what I understand,
JET defines Q to be the ratio of fusion power produced to the
heating power that actually heated the plasma. TFTR usually uses
a different accounting method: they use the ratio of fusion power to
heating power injected into the plasma. Typically to convert Q from JET
accounting to TFTR accounting you divide by two as perhaps 50% or so
of the heating power actually heats the plasma in a useful way, the rest 
might actually cool it down. The JET method is somewhat justified if
you can find ideal heating sources.

To further complicate things, as tokmaks usually use 100% Deuterium rather
than a 50% Deuterium-50% Tritium mixture, people frequently ``extrapolate''
from DD to DT, i.e.  to estimate the Q from a DD shot they calculate the Q
from a DT shot that has the same parameters as the DD shot. Typically
this increases Q by a factor of around 200.

So, here are some Q numbers (using JET accounting). The highest unextrapolated
Q (i.e. using some tritium) is about 0.15. The highest extrapolated Q (using
DD) is about 1.15. TFTR's highest Q is about 0.4 using TFTR accounting and
perhaps as high as 0.8 using JET accounting.

>4.  What is the most probable method for obtaining usable energy from the
>   resultant plasma?  Or is the answer, "hell, we'll cross that bridge when
>   we come to it?"

Burning the paperwork required to put tritium in a tokamak might be able to
heat a small town for a few years...

	Scott

P.S. A fusion textbook such as Miyamoto will probably clarify some of these
issues. The JET results were published in Nuclear Fusion, vol 32 p 187, 1992.
Xref: sparky sci.physics.fusion:2402 sci.physics:16171