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ExB Corrections for the STAR and ALICE TPCs

ExB Corrections for the STAR and ALICE TPCs. Jim Thomas 24 - February – 2011. Solve:. Microscopic Lorentz force with “Friction”. substituting:. subject to the steady state condition. yields. where B is a unit vector pointing in the direction of B.

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ExB Corrections for the STAR and ALICE TPCs

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  1. ExBCorrections for the STAR and ALICE TPCs Jim Thomas 24- February– 2011

  2. Solve: Microscopic Lorentz force with “Friction” substituting: subject to the steady state condition yields where B is a unit vector pointing in the direction of B. The Langevin Equation – (see Blum, Riegler and Rolandi)

  3. Simple first order equations An Example: The Case of E  Parallel to B Electric field strength cancels out! Small terms  2nd order corrections Assuming cylindrical coordinate and E = Ezand Bz >> Br or Bf

  4. Distortion Equations – related to integrals of the fields Distortion in x or y Integral over distorted field Master Equations for E or B field distortions simple linear equations with • Distortions in the TPC are directly related to integrals of the E and B fields • These solutions of the Langevin Equation are exact to 2nd order • The matrices are rotations (with a pre-factor) related to the Lorentz angle • Since rotations commute in 2 dimensions, these matrices commute with other rotations. These same equations are valid in Cylindrical Coordinates, x  r, y r *  If you have a well defined model, and good data, then the distortion can be removed with great precision

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