Runaway electrons

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Runaway electrons

• Leena Aho-Mantila

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What are runaway electrons?

• Electrons that run away in velocity space
• Charged particles undergo Coulomb collisions,
  collisionality decreases with energy
• If the energy of a single charged particle is
  high enough, it may propagate independently of
  the bulk particles

Collisions drive the electrons toward an
equilibrium distribution
Accelerated electron beam detached from the main
body of the distribution
High-energy electrons undergo least collisions
and may become independent of the bulk of the
distribution
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Principle of Runaway

• Forces experienced by a single particle
• Electric field accelerates charged particles (FE)
• Acceleration is suppressed by a collisional drag
  force (Fcoll)
• Sudden application of an electric field
• Electrons may gain a critical velocity vcrit
  before experiencing a collision
• Fcoll decreases as v3
• Above vcrit, FE gtFcoll and the electrons are
  further accelerated

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When is this an issue?

• Sudden changes in the toroidal electric field
• Current ramp-up
• Disruptions
• High electric field might accelerate even the
  bulk of the electrons, if ve-vigtvth
• At this drift velocity, collisional force between
  the two species starts to decrease
• No runaway process for small electric fields
• Slowing-down time becomes constant at
  relativistic speed

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Consequences

• Runaway electrons are accelerated to a maximum
  energy at which synchrotron radiation
  (brehmsstrahlung by relativistic particles)
  starts to dominate
• Typically results in a monoenergetic beam of
  electrons that diffuces radially until it
  contacts a material surface
• emax might be around 105 keV, enough to cause
  serious damage to the wall structure
• Other mechanisms can also limit the maximum
  energy, such as resonance interaction between
  gyromotion and magnetic field ripple (increases
  v- and radiation)
• Close collisions between runaway and thermal
  electrons may bring more electrons to the runaway
  velocities
• Might be of special concern in disruptions
  occurring in future large tokamaks

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Results from FTU

• Parameters
• Plasma current Ip0.3 1 MA
• Toroidal magnetic field B57 T
• Zeff26
• Line averaged density up to 1x1020 m3.
• Runaway electrons are generated during current
  ramp-up and observed for the whole discharge
  time, mainly in the core plasma
• Maximum runaway energies 10-20 MeV

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References

• Wesson, Tokamaks p. 72
• Chen, Introduction to Plasma Physics and
  Controlled Fusion p. 182
• A. Esposito et al, Dynamics of high energy
  runaway electrons in the Frascati Tokamak
  Upgrade, Physics of Plasmas 10 (2003)
• Z. Chen et al, Energy limit of runaway electrons
  in the HT-7 tokamak, Phys. Rev. Letters A 351
  (2006)