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Setting of Focused Beam in MARS for Meson Production Optimization

Setting of Focused Beam in MARS for Meson Production Optimization. X. Ding, UCLA AAG Meeting. Focused Incident Proton Beam at 8 GeV. Focused Incident Proton Beam at 8 GeV (Cont’d). Non-Linear Fit (Growth/sigmoidal, Hill) Y=N/(1+K2/beta -2 ) N=1.018 Sqrt(K2)=0.1368

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Setting of Focused Beam in MARS for Meson Production Optimization

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  1. Setting of Focused Beam in MARS for Meson Production Optimization X. Ding, UCLA AAG Meeting

  2. Focused Incident Proton Beam at 8 GeV

  3. Focused Incident Proton Beam at 8 GeV (Cont’d) Non-Linear Fit (Growth/sigmoidal, Hill) Y=N/(1+K2/beta-2) N=1.018 Sqrt(K2)=0.1368 Linear emittance is 4.8 μm with beam radius of 0.12 cm and β* of 0.3 m.

  4. Gaussian distribution(Probability density) • In two dimensional phase space (u,v): where u-transverse coordinate (either x or y), v=αu+βu’ α, β are the Courant-Synder parameters at the given point along the reference trajectory. In polar coordinates (r, θ): u=rcosθ v=rsinθ u’=(v-αu)/β=(rsinθ-αu)/β

  5. Distribution function method Random number generator: θ=2π*rndm(-1) r=sqrt(-2*log(rndm(-1))*σ

  6. Gaussian distribution(Fraction of particles) • The fraction of particles that have their motion contained in a circle of radius “a” (emittance ε=πa2/β) is

  7. Fraction of particles Normalized emittance: (βγ)εKσ

  8. Focused beam • Intersection point (z=-37.5 cm): α*= 0, β*, σ* • Launching point (z=-200 cm): L=200-37.5=162.5 cm α=L2/β* β=β*+L2/β* σ=σ*sqrt(1+L2/β*2)

  9. Setting of simple Gaussian distribution • INIT card in MARS.INP (MARS code) INIT XINI YINI ZINI DXIN DYIN DZIN WINIT XINI=x0 DXIN=dcx0 YINI=y0 DYIN=dcy0 ZINI=z0 DZIN=dcz0=sqrt(1-dcx02-dcy02) (Initial starting point and direction cosines of the incident beam)

  10. Setting with focused beam trajectories • Modeled by the user subroutine BEG1 in m1510.f of MARS code xv or xh (transverse coordinate: u); xvp or xhp (deflection angle: u’) XINI=x0+xv DXIN=dcx0+xvp YINI=y0+xh DYIN=dcy0+xhp ZINI=z0 DZIN=sqrt(1-DXIN2-DYIN2)

  11. Optimization of target parameters • Fixed beam emittance (εKσ?) choice of (σ*, k, β*) at different KE? • Optimization method (Target radius & beam radius is fixed? Only Vary beam/jet angle and beam angle in each cycle?)

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