Target density

Goran Skoro

12 November 2008

A Simple Model for Pion Yield from the Target

Assume that the number of pions produced per proton hitting the target is p and that the fraction of pions absorbed in the target is a. Then, the yield of pions for a solid target is,

Y = p(1-a)

and for a target of the same geometry and material

but density f, is,

Yf = fp(1-fa)

The ratio,

R = Yf /Y=f(1-fa)/(1-a)

is shown here as f varies.

N.B. No magnetic field. Acceptance not included.

Roger Bennett’s model*

*http://www.hep.princeton.edu/~mcdonald/mumu/target/bennett/bennett_110608b.pdf

Rati

o o

f p

ion

yie

lds,

R =

Y(

targ

et/Y

(tu

ng

ste

n

Density ratio, f = target/tungsten

Model vs. MARS simulations

MARS: 10 GeV protons,parabolic beam,target length = 25 cm,target diameter = 2 cm.

Yields are from target surface, not downstream.

John Back’s ICOOL probability acceptance map*

*http://hepunx.rl.ac.uk/uknf/wp3/pimuyields/pimuYield_12Jun08.pdf

These pions vs. model?

Case I: all pions

Case II: forward pions

TARGETp beam

pions

TARGETp beam

pions

Model vs. MARS simulations – Case I

TARGETp beam

pions

Model vs. MARS simulations – Case I

TARGETp beam

pions

Model vs. MARS simulations – Case II

TARGETp beam

pions

Model vs. MARS simulations – Case II

TARGETp beam

pions