Stopping Power for Arbitrary Angle Between Nuclear Alpha

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• Stopping Power for Arbitrary Angle Between
  Nuclear Alpha
• Velocity and Magnetic Field
• Carlo Cereceda
• Depto. Fisica, Universidad Simon Bolivar, Apdo.
  89000, Caracas, Venezuela
• Michel de Peretti
• CPL,EPF Ecole d'Ingenieurs, 3 bis rue Lakanal,
  92330, Sceaux, France
• Claude Deutsch
• LPGP (UMR-CNRS) Bat. 210, Universite de
  Paris-Sud, 91405 Orsay, France

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Introduction

• In a previous work 1 we calculated a numerical
  stopping power for alpha
• particles in movement parallel to the magnetic
  field.
• Here, a numerical approached study shows the
  convergence of the series
• in the general stopping power expression for a
  finite but large number of terms.
• This calculations require a large CPU time but
  they will allow the simulation of the
• particles trajectory in simulations.

• Stopping power of particles in helical movement
  in a magnetic field

• The inversion of the fluctuation-dissipation
  theorem, let study the high frequency properties
  of the plasma.
• The dielectric function obtained by kinetic
  theory does not neglects low frequency phenomena.

• with

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• In previous works 1, 2, 3 we calculated the
  stopping power of test particles by following the
  helical trajectory that yields a charge density

• Giving the Stopping Power

• The numerical calculation of the integration on
  is harder to do due to the oscillating
  behavior of the Bessel function. We have verified
  that by first adding
• on , the oscillations of the function to be
  integrated are smoother, and that the
• series converges for a finite but large number of
  terms

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• The series on is rapidly convergent for a
  few number of terms in the studied cases.
• The integrand I of the stopping power is plotted
  as a function of parallel and perpendicular wave
  number components, in order to approximately
  determine the maximum number of terms L to be
  taken in the series and the practical limit in
  the infinite integration.

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• Alpha particles from D-T fusion in magnetized
  plasma
• For alpha particles produced by D-T fusion
  reaction in a hot plasma with
• temperatures in the order of keV and strong
  magnetic fields in the order of several
• Tesla as in the MTF approach, the Larmor radius
  is larger than the Debye length
• and we have to integrate until the inverse of the
  minimum distance of closest
• approach.
• Figure below shows the maximum height of the
  integrand I for various L
• with N 8 and u v/vTe 2. It reaches its
  maximum value around L 210.

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• In the following figures we show the stopping
  power for angles q 0, p /8, p /4, 3p/8 and 1.5
  respect to B as a function of u.

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• Range of alpha particles
• D-T fusion generated alpha particles enter the
  plasma with a maximum starting isotropic velocity
  corresponding to the creation energy of 3.5 MeV
  which dimensionless value is umax 0.3 for the
  plasma fusion temperatures of the order of keV.
• Detailed calculations of the stopping power of
  alpha particles with velocities in this range 0,
  0.3, let us calculate the range along the
  elliptic path with diminishing Larmor radius

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• The range is very short for movement parallel to
  the magnetic field but it increases quickly from
  an angle of p /8 until very large values found by
  other
• theories 4.

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CONCLUSION These reliable and sufficiently
accurate calculations will allow to investigate
the trajectory of alpha particles with reducing
Larmor radius leading to a determination of the
contribution of thermonuclear alpha particles to
the ignition of magnetized plasma
target. References 1.- C. Cereceda, C. Deutsch,
M. dePeretti, M. Sabatier, H. Nersisyan. Physics
of Plasmas, 7, 2884 (2000). 2.- H. Nersisyan.
Phys. Rev. E, 58, 3686 (1998). 3.- H. Nersisyan,
C. Deutsch. Phys. Letters A, 246, 325
(1998). 4.- C. Deutsch, H. Nersysian, C.
Cereceda. Laser and Particle Beams, 20, 463(2003).