Numerical Model of an Internal Pellet Target

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Numerical Model of an Internal Pellet Target
O. Bezshyyko, K. Bezshyyko, A. Dolinskii,I. Kad
enko, R. Yermolenko, V. Ziemann Nuclear
Physics Department, Taras Shevchenko National
University GSI, 64287,Darmstadt,
Germany Svedberg Laboratory, Uppsala University,
S-75121Uppsala, Sweden
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Pellet Target

• Beam of small frozen hydrogen pellets
• Shape of pellet nearly spheres
• Pellet diameter 30 µm (20 - 70 µm)
• ?H0.0708 g /cm2
• Mass of 1 pellet 10-9 g (d30 µm)
• Number of atoms in 1 pellet 51014 (d30 µm)
• Pellet generation rate 50 kHz (20 - 80 kHz)

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Pellet Target

• Vertical velocity 50 m/s
• Distance between pellets 1 mm (rate 60 kHz,
  Vv 50 m/s)
• Angle divergence of pellet beam 0.040
• Distance between injection nozzle and area of
  beam dozens of cm (real example 241 cm)
• Spread of pellet beam in the point of crossing
  with antiproton beam 1 (1 - 3)

Pellet beam
Ion beam
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Internal target effects

• Small angle scattering
• Energy loss, energy straggling (relative momentum
  straggling ?p/p)

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Coulomb Multiple Scattering

• Moliere theory (with various modifications)
  widely used approach
• Main restriction to Moliere theory number of
  scatters O020
• - parameters of Moliere theory,
• - critical scattering angle
• - atomic electron screening
  angle
• - incident particle charge
• - total path length in the
  scatterer
• O0?2 for pellets with diameter ?30 ?m
• This value is out of area of Moliere theory
  application
• 1ltO0lt20 Plural Scattering approach (direct
  simulation method), used by GEANT toolkit

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Plural Scattering algorithm

• Calculation of scatters number n. Poisson
  distribution with average
• Generation of random number - angle of the
  single scattering
• This approximates Rutherford
  distribution
• where is a random number uniformly
  distributed in the interval between 0 and 1
• Generation of random number (uniformly
  distributed in the interval between 0 and 2?)
  to project the scattering angle into the
  horizontal (or vertical) direction.
• Calculation of total scattering angle for one
  hit
• 
  for horizontal direction
  
  for vertical direction
• 
  

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Numerical results

• Scattering angle distribution for Plural
  scattering and simple Moliere scattering

RMS scattering angle dependence on diameter of
pellet
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Energy losses and straggling

• Main parameters for choice between theories
• 1.
  2.
• - mean energy
  loss
• - maximum
  transferable energy in single collision with an
  atomic electron
• - mean ionization
  potential of the atom
• - the electron mass
• - the mass of the
  incident particle
• - charge of the
  incident particle
• - atomic number and
  weight of the target
• - density of the
  target
• - thickness of the
  target

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Conditions for choice of the model

• Area of Gauss distribution
• Area of Vavilov distribution

Area of Landau distribution
Pellet target
for E1 GeV, d30 µm
It is necessary to take into account atomic
structure and direct simulation of scattering
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Urban model

• Algorithm
• Calculation of
• Calculation of ni (Poisson distribution)
• Calculation of excitation energy loss
• Calculation of ionisation energy loss
• Calculation of the total energy loss
• Calculation of the relative momentum straggling

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Urban model
f1f11 f1lnE1 f2lnE2 lnI
f1,2 oscilator strengths Macroscopic
cross-section for exitation (i1,2) Macroscopic
cross-section for ionisation Distribution of
ionisation energy loss Approximation of g(E)
distribution is a random
number uniformly distributed between 0 and 1

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Subroutine features

• Detail 2D (in plane normal to beam axis)
  geometrical description of particle interaction
  with pellet is applied
• Spatial distribution of pellet beam in the
  interaction area is recalculated through spatial
  and angle distribution at the injection nozzle
• The local (not mean value) thickness of pellet is
  taken into account
• Main input parameters - x,y,x,y, energy of
  particle, parameters of the pellet beam
• Output data dp/p (relative momentum straggling
  ) and (total scattering angle )
  projections into the horizontal and vertical
  direction

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Numerical test results
RMS dE distribution
Emax dependence on pellet diameter
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Numerical test results
dp/p dependence on pellet diameter
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Conclusions

• Program block for Monte Carlo simulation of the
  pellet target is developed
• Plural Scattering model for simulation of angle
  distributions during every turn analysis is used
• Urban model for simulation of energy losses
  during every turn analysis is used
• Moliere theory and Landau (Vavilov, Gauss) models
  are preferable only in cases of analysis of
  target effects after dozens and more turns
• Detailed 2D (in plane normal to beam axis)
  geometrical description of particle interaction
  with pellet is applied
• Preliminary numerical results to check the code
  are obtained, extended tests of code as part of
  some Monte Carlo codes for analysis of beam
  parameters are planned in the near future

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Ionisation/Excitation ratio, r
Ionisation/Excitation ratio, r
RMS dE dependence on Ionisation/Excitation ratio
RMS dE dependence on Ionisation/Excitation ratio
(log scale)