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Physics of fusion power. Lecture 3: Lawson criterion / Approaches to fusion. Ignition condition. Ignition is defined as the state in which the energy produced by the fusion reactions is sufficient to heat the plasma. n-T-tau is a measure of progress.

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Physics of fusion power

Physics of fusion power

Lecture 3: Lawson criterion /

Approaches to fusion


Ignition condition
Ignition condition

  • Ignition is defined as the state in which the energy produced by the fusion reactions is sufficient to heat the plasma.


N t tau is a measure of progress
n-T-tau is a measure of progress

  • Over the years the n-T-tau product shows an exponential increase

  • Current experiments are close to break-even

  • The next step ITER is expected to operate well above break-even but still somewhat below ignition


Some landmarks in fusion energy research
Some landmarks in fusion energy Research

  • Initial experiments using charged grids to focus ion beams at point focus (30s).

  • Early MCF devices: mirrors and Z-pinches.

  • Tokamak invented in Russia in late 50s: T3 and T4

  • JET tokamak runs near break-even 1990s

  • Other MCF concepts like stellarators also in development.

  • Recently, massive improvements in laser technology have allowed ICF to come close to ignition: planned for last year but didn’t happen.



Quasi neutrality
Quasi-neutrality

  • Using the Poisson equation

  • And a Boltzmann relation for the densities

  • One arrives at an equation for the potential

Positive added charge Response of the plasma


Solution
Solution

  • The solution of the Poisson equation is

Potential in vacuum Shielding due to the charge screening

The length scale for shielding is the Debye length which depends on both Temperature as well as density. It is around 10-5 m for a fusion plasma

Vacuum and plasma solution


Quasi neutrality1
Quasi-neutrality

  • For length scales larger than the Debye length the charge separation is close to zero. One can use the approximation of quasi-neutrality

  • Note that this does not mean that there is no electric field in the plasma

  • Under the quasi-neutrality approximation the Poisson equation can no longer be used to calculate the electric field


Divergence free current
Divergence free current

  • Using the continuity of charge

  • Where J is the current density

  • One directly obtains that the current density must be divergence free


Also the displacement current must be neglected
Also the displacement current must be neglected

  • From the Maxwell equation

  • Taking the divergence and using that the current is divergence free one obtains

  • The displacement current must therefore be neglected, and the relevant equation is


Quasi neutrality2
Quasi-neutrality

  • The charge density is defined to be equal to zero (but a finite electric field does exist)

  • This equation replaces the Poisson equation. (we do not calculate the electric field from Poisson’s equation, which would give zero field)

  • Additionally, the displacement current is neglected.

  • Length scales of the phenomena are larger than the Debye length, time scales longer than the plasma frequency.

  • The current is divergence free.


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