Physics of fusion power

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Physics of fusion power

• Lecture 3 Lawson criterion /
• Approaches to fusion

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Ignition condition

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

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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

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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 didnt
  happen.

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Alternative fusion concepts
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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
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Solution

• The solution of the Poisson equation is

Potential in vacuum Shielding due to the
charge screening
Vacuum and plasma solution
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
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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

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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

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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

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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
  Poissons 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.