# Test Ring for Ionization Cooling

![](media/image1.wmf){width="5.895833333333333in"
height="3.0520833333333335in"}

Beta-functions and dispersions

![](media/image2.wmf){width="5.895833333333333in" height="3.21875in"}

Beam envelopes for acceptance of ε=4106 mm mrad and momentum spread of
∆p/p=0.01

Parameters at the end of the lattice (target center)

BetaX\[cm\]=25.0109 BetaY\[cm\]=25.0365

AlfaX=3.24266e-07 AlfaY=-1.45101e-07 Qx=1.73298 Qy=1.73861

DispX\[cm\]=223.904 DispY\[cm\]=0

DispPrX=7.11707e-07 DispPrY=0

Energy=999.405

Momentum Compaction=-0.367054

### Optim file

\$P0=1100; =\> 1100

\$m=105.658; =\> 105.658

\$E0=sqrt(\$P0\*\$P0+\$m\*\$m)-\$m; =\> 999.404719

\$gamma=1+\$E0/\$m; =\> 10.4588646

\$beta=sqrt(1-1/\$gamma/\$gamma); =\> 0.995418614

\$Hr=\$P0/\$c\*1e11; =\> 3669.20453

\$F=201.25e6; =\> 201250000

\$Lambda=\$c/\$F; =\> 148.965217

#Cooling

\$LenCool=60; =\> 60

\$BetaStar=25; =\> 25

\$BetaStarOpt=\$LenCool/2/sqrt(3); =\> 17.3205081

\$BetaEff=\$BetaStar+\$LenCool\*\$LenCool/\$BetaStar/12; =\> 37

\$EnLoss=0.28\*\$LenCool; =\> 16.8

\$NCool=2\*\$E0/\$EnLoss; =\> 118.976752

#Equilibrium emittance

\$EmitN=\$Me/\$m\*\$BetaEff\*\$beta; =\> 0.17812755

\$Emit=\$EmitN/\$gamma/\$beta; =\> 0.017109637

\$Accept=\$Emit\*6\*4; =\> 0.410631288

\# Beam life time due to decay

\$TauDecay=2.2e-6; =\> 2.2e-06

\$C=3724.53; =\> 3724.53

\$NTurn=\$gamma\*\$TauDecay\*\$beta\*\$c/\$C; =\> 184.358119

\# Synchrotron frequency

\$FiAccel=60/180\*\$PI; =\> 1.04719755

\$V0=\$EnLoss/sin(\$FiAccel) ; =\> 19.398969

\$Alpha=0.367; =\> 0.367

\$q=\$C/\$Lambda; =\> 25.0026823

\$NuS=sqrt(\$q\*\$V0\*cos(\$FiAccel)\*\$Alpha/(2\*\$PI\*\$E0)); =\>
0.119052914

\$dPoverP=0.002; =\> 0.002

\$SigmaS=\$Alpha/\$NuS\*\$C/(2\*\$PI)\*\$dPoverP; =\> 3.65466556

\$SigmaFi=\$SigmaS/\$Lambda\*360; =\> 8.8321262

\$SigmaFiTot=\$SigmaFi\*2.5\*2; =\> 44.160631

\$dPoverPTot=\$dPoverP\*2.5\*2; =\> 0.01

\#

\$B=13; =\> 13

\$L=\$Hr/\$B\*\$PI/4; =\> 221.675885

\$bb=\"g bb g od g bb g\"; =\>g bb g od g bb g

OptiM

Energy\[MeV\]=999.40472 Mass\[MeV\]=105.658

Emittance: ex\[cm\]=\$Accept ey\[cm\]=\$Accept DP/P=\$dPoverPTot

Initial: BetaX\[cm\]=25.011 BetaY\[cm\]=25.0364

AlfaX=-4.18726e-17 AlfaY=-2.08701e-16

DispersX\[cm\]=223.904 DispersY\[cm\]=0

Dsp_PrimeX=7.63326e-16 DspPrimeY=0

X\[cm\]=0.000 Y\[cm\]=0.000 Z\[cm\]=0.000 S\[cm\]=0.000

tetaX\[deg\]=0 tetaY\[deg\]=0

\# Elements: O,I-drift, D,B-sector dipole, G-magnet edge

\# Q-quad, S-sextipole, C,CC-solenoid and its focusing part only

\# M-multipole(length=0), K,Z-transverse and longitudinal correctors

\# A,W-RF cavity(standing wave), E-electroctatic acc.section

\# X-transfer matrix (next 6 lines have to hold the matrix itself)

\# R-combined magneto-electrostatic bend, L - electrostatic quad

\# F-Litium lens, H-Scraper or aperture

begin lattice. Number of periods=1

iAbsorb o cc1 o2 \$bb o1 q2f o1 \$bb o3 cc2 o4

o4 cc2 o3 \$bb o1 q2f o1 \$bb o2 cc1 o iAbsorb

end lattice

begin list

iAbsorb L\[cm\]=30

o L\[cm\]=20

od L\[cm\]=10

o1 L\[cm\]=60

o2 L\[cm\]=212.78

o3 L\[cm\]=100

o4 L\[cm\]=212.78

bb L\[cm\]=\$L B\[kG\]=\$B G\[kG/cm\]=0 Tilt\[deg\]=0

g B\[kG\]=\$B Angle\[deg\]=11.25 EffLen\[cm\]=0 Tilt\[deg\]=0

cc1 L\[cm\]=130 B\[kG\]=72 Aperture\[cm\]=20

cc2 L\[cm\]=80 B\[kG\]=49 Aperture\[cm\]=20

q2f L\[cm\]=50 G\[kG/cm\]=-0.004 Tilt\[deg\]=0

end list of elements