Optimized Target Parameters and Meson Productions of IDS120h with Focused Gaussian Beam and Fixed Em...
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Optimized Target Parameters and Meson Productions of IDS120h with Focused Gaussian Beam and Fixed Emittance. X. Ding, UCLA AAG Meeting. Focused Incident Proton Beam at 8 GeV. Normalized meson production is 0.84 at β* of 0.3 m. Focused Incident Proton Beam at 8 GeV (Cont’d). Non-Linear Fit

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Optimized Target Parameters and Meson Productions of IDS120h with Focused Gaussian Beam and Fixed Emittance

X. Ding, UCLA

AAG Meeting


Focused incident proton beam at 8 gev
Focused Incident Proton Beam at 8 GeV with Focused Gaussian Beam and Fixed Emittance

Normalized meson production is 0.84 at β* of 0.3 m.


Focused incident proton beam at 8 gev cont d
Focused Incident Proton Beam at 8 GeV (Cont’d) with Focused Gaussian Beam and Fixed Emittance

Non-Linear Fit

(Growth/sigmoidal, Hill)

Y=N/(1+K2/beta-2)

N=1.018

Sqrt(K2)=0.1368

Linear emittance is 4.9 μm with beam radius of 0.1212 cm and β* of 0.3 m.


Gaussian distribution probability density
Gaussian distribution with Focused Gaussian Beam and Fixed Emittance(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


Distribution function method
Distribution function method with Focused Gaussian Beam and Fixed Emittance

Random number generator:

θ=2π*rndm(-1)

r=sqrt(-2*log(rndm(-1))*σ


Gaussian distribution fraction of particles
Gaussian distribution with Focused Gaussian Beam and Fixed Emittance(Fraction of particles)

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


Fraction of particles
Fraction of particles with Focused Gaussian Beam and Fixed Emittance

Normalized emittance: (βγ)εKσ


Focused beam
Focused beam with Focused Gaussian Beam and Fixed Emittance

  • Intersection point (z=-37.5 cm):

    α*= 0, β*, σ*

  • Launching point (z=-200 cm):

    L=200-37.5=162.5 cm

    α=L/β*

    β=β*+L2/β*

    σ=σ*sqrt(1+L2/β*2)


Setting of simple gaussian distribution
Setting of simple Gaussian distribution with Focused Gaussian Beam and Fixed Emittance

  • 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)


Setting with focused beam trajectories
Setting with focused beam trajectories with Focused Gaussian Beam and Fixed Emittance

  • 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)


Optimization of target parameters
Optimization of target parameters with Focused Gaussian Beam and Fixed Emittance

  • Fixed beam emittance (εKσ) to π(σ)2/β

  • Optimization method in each cycle

    (Vary beam radius or beam radius σ*, while vary the β* at the same time to fix the beam emittance; Vary beam/jet crossing angle; Rotate beam and jet at the same time)

    We also optimized the beam radius and target radius separately (not fixed to each other).


Effect of solenoid field calculation of at z 200cm
Effect of Solenoid Field with Focused Gaussian Beam and Fixed Emittance(Calculation of α, β, σ at z=-200cm)


Effect of solenoid field calculation of at z 200cm1
Effect of Solenoid Field with Focused Gaussian Beam and Fixed Emittance(Calculation of α, β, σ at z=-200cm)


Courant snyder invariant
Courant-Snyder Invariant with Focused Gaussian Beam and Fixed Emittance


Optimized target parameters and meson productions at 8 gev linear emittance is fixed to be 4 9 m
Optimized Target Parameters and Meson Productions at 8 GeV with Focused Gaussian Beam and Fixed Emittance(Linear emittance is fixed to be 4.9 μm )


Optimize beam radius and target radius separately
Optimize beam radius and target radius separately with Focused Gaussian Beam and Fixed Emittance

We found almost no improvement in optimized meson production if the beam radius is not fixed at 30% of target radius and optimized separately!


Optimized meson productions at 8 gev linear emittance is fixed to be 4 9 m
Optimized Meson Productions with Focused Gaussian Beam and Fixed Emittanceat 8 GeV(Linear emittance is fixed to be 4.9 μm )


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