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An analytic formula for track extrapolation in an inhomogeneous magnetic field

KIP. An analytic formula for track extrapolation in an inhomogeneous magnetic field. Sergey Gorbunov Ivan Kisel DESY, Zeuthen KIP , Uni-Heidelberg. ACAT 2005, DESY, Zeuthen May 22-27, 2005. Extrapolation in Magnetic Field.

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An analytic formula for track extrapolation in an inhomogeneous magnetic field

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  1. KIP An analytic formula for track extrapolation in an inhomogeneous magnetic field Sergey Gorbunov Ivan Kisel DESY, Zeuthen KIP, Uni-Heidelberg ACAT 2005, DESY, Zeuthen May 22-27, 2005

  2. Extrapolation in Magnetic Field Differential equation of charged particle motion in a magnetic field Along Z direction : S. Gorbunov, I. Kisel

  3. Analytic Expression Coefficients: Equation of motion: Extrapolation error: S. Gorbunov, I. Kisel

  4. Analytic Expression Features B(z) Real track (theoretically) Track guess (practically) B( (z0+z)/2 ) B(z0) z0 z (z0+z)/2 • Features : • Field is taken as a function of z coordinate. S. Gorbunov, I. Kisel

  5. Analytic Expression Features • Features : • The precision of extrapolation does not depend on a shape of the magnetic field. • One can cut off the higher-order terms in the series. S. Gorbunov, I. Kisel

  6. Analytic 3 Example: Third order extrapolation in a homogeneous By field Small parameter: S. Gorbunov, I. Kisel

  7. Coefficients in the Analytic Formula (CBM) Analytic Light Analytic 1 Analytic 2 Analytic 3 S. Gorbunov, I. Kisel

  8. Performance of Extrapolation (CBM) S. Gorbunov, I. Kisel

  9. Implementation in CBM CA Track Finder ALL MC TRACKS RECONSTRUCTABLE TRACKS Number of hits >= 4 REFERENCE TRACKS Momentum > 1 GeV S. Gorbunov, I. Kisel

  10. Conclusion • An analytic formula of extrapolation in magnetic field has been derived • Precision of extrapolation does not depend on a shape of the field. • The implementation in the CBM track fitting procedure has the same accuracy as the fourth-order Runge-Kutta method. S. Gorbunov, I. Kisel

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