# Lawson's Criterion: Applying to Plasmas & Deriving its Basis

• sid_galt
In summary, Lawson's criterion is a rough estimate for the conditions required for fusion and applies to all fusion schemes, regardless of the confinement mechanism. It is derived from basic fusion principles and takes into account plasma density, temperature, and confinement time. While different fusion schemes may have different combinations of these factors, all must fulfill the Lawson criterion in order to achieve fusion.
sid_galt
What is the basis for Lawson's criterion? How is it derived?

Does it apply to all plasmas or only to magnetically confined plasmas?

sid_galt said:
What is the basis for Lawson's criterion? How is it derived?

Does it apply to all plasmas or only to magnetically confined plasmas?

Sid,

Lawson's criterion is a rough estimate for the conditions required for
fusion - any basic fusion text will give you the details.

It applies for ALL fusion schemes - regardless of the confinement
mechanism. It's interesting to see how the various fusion schemes
fulfill the Lawson criterion.

Take magnetic confinement. In magnetic confinement, the plasma
densities are fairly low - anyone else would call them a pretty good
vacuum. But the confinement times are on the order of a second or
a few seconds.

At the other end of the spectrum is inertial confinement fusion - also
called "laser fusion". Here there is no attempt made to try to confine
the plasma - only the plasma's own inertia limits its expansion.
Confinement times here are extremely small - on the order of
nanoseconds. However, the densities are extremely high - on the order
of 10,000 grams per cubic centimeter. So the product can also fulfill
the Lawson criterion.

So we have two extremes - low density, but high confinement time
[ magnetic fusion ] or high density, low confinement time [ inertial
confinement fusion ]

Dr. Gregory Greenman
Physicist

sid_galt said:
What is the basis for Lawson's criterion? How is it derived?

Does it apply to all plasmas or only to magnetically confined plasmas?

## 1. What is Lawson's Criterion and how does it apply to plasmas?

Lawson's Criterion is a measurement used to determine the minimum conditions required for a plasma to sustain a fusion reaction. It takes into account the rate of energy lost through radiation and the rate of energy produced through fusion. If the energy produced is greater than the energy lost, the plasma can sustain the fusion reaction.

## 2. How is Lawson's Criterion derived?

Lawson's Criterion is derived from the balance between the energy produced through fusion and the energy lost through radiation. It takes into account the confinement time, density, and temperature of the plasma. The equation for Lawson's Criterion is Pτ ≥ 3/2nkT, where P is the power produced, τ is the confinement time, n is the density, k is the Boltzmann constant, and T is the temperature.

## 3. Why is Lawson's Criterion important in fusion research?

Lawson's Criterion is important because it provides a benchmark for determining the feasibility of a fusion reaction. It helps scientists determine the minimum conditions required for a plasma to sustain a fusion reaction, which is crucial for the development of fusion energy as a viable source of clean and renewable energy.

## 4. How does improving confinement time affect Lawson's Criterion?

A longer confinement time means that the plasma can sustain the fusion reaction for a longer period of time, which allows for more energy to be produced. This means that the left side of the Lawson's Criterion equation (Pτ) will increase, making it easier to meet the minimum requirements for sustaining a fusion reaction.

## 5. How does Lawson's Criterion differ from the Bremsstrahlung power loss criterion?

The Bremsstrahlung power loss criterion only considers the energy lost through radiation, while Lawson's Criterion takes into account both the energy produced through fusion and the energy lost through radiation. This makes Lawson's Criterion a more comprehensive measurement for determining the feasibility of a fusion reaction in a plasma.

• Nuclear Engineering
Replies
19
Views
2K
• Nuclear Engineering
Replies
3
Views
1K
• Nuclear Engineering
Replies
5
Views
2K
• Nuclear Engineering
Replies
13
Views
2K
• High Energy, Nuclear, Particle Physics
Replies
1
Views
943
• Nuclear Engineering
Replies
4
Views
2K
• High Energy, Nuclear, Particle Physics
Replies
9
Views
2K
• Aerospace Engineering
Replies
1
Views
2K
• Other Physics Topics
Replies
2
Views
389
• Nuclear Engineering
Replies
1
Views
2K