How to check the proton csda range ?

Jean Jacquemier, Michel Maire

LAPP (Annecy) August 2006

Geant4 Workshop, Lisbon 9-14 October 2006 2

Csda range

Full = unrestricted = no delta-rays generationinfinity cut (> maximum transferable energy)

In addition :no energy fluctuation (straggling)no multiple scattering

0

1( ) ( ) = Bethe - Bloch formula( ) ful

e E

le

dER E de f ef e dx

=

=

⎛ ⎞⎟⎜= ≡ ⎟⎜ ⎟⎜⎝ ⎠⌠⎮⌡

Geant4 Workshop, Lisbon 9-14 October 2006 3

nist : 7.718 g/cm2

proton 100 MeV in water

Geant4 Workshop, Lisbon 9-14 October 2006 4

Csda range : Geant4 / Nist

Geant4 Workshop, Lisbon 9-14 October 2006 5

Projected range : Geant4 / Nist

Geant4 Workshop, Lisbon 9-14 October 2006 6

Nb steps : lowE / stand

~15

Geant4 Workshop, Lisbon 9-14 October 2006 7

Geant4: e- step limitation from physics

Ionization and brems• production threshold aka Cut

indirect effect : the mean free path between discrete interactions depend of Cut

Continuous energy loss• Max fractional energy loss per step. dR/R < dRoverRange• Down to a certain limit : finalRange

Multiple scattering• Limit defined at first step and reevaluated after a boundary, to

allow back scattering of low energy e-

step = fr.max(range,λ) fr = facRange• Geometry : force more than 1 step in any volume : facGeom

Geant4 Workshop, Lisbon 9-14 October 2006 8

Step limitation from continuous energy loss

The cross sections depend of the energy. The step size must be small enough to ensure a small fraction of energy loss along thestep :

This constraint must be relaxed when E 0

stepRange(E)

dRoverRange≤

finalRange

Geant4 Workshop, Lisbon 9-14 October 2006 9

proton 100 MeV in water

standard lowE

12 steps ~ 200 steps

Geant4 Workshop, Lisbon 9-14 October 2006 10

proton 100 MeV in water

time : lowE / stand > 10

nist : 77.18 mm

nist : 77.07 mm

~ 1 mm

csda condition

Geant4 Workshop, Lisbon 9-14 October 2006 11

Is range shifting with cuts-values?

Stopping depth of 250 MeV proton in Water

0

200

400

600

800

1000

1200

350 360 370 380 390 400Depth [mm]

relat

ive n

umbe

r

with MCS 1mmwith MCS 0.1mmwith MCS 0.01mmwith MCS 0.001mmwithout MCS 1mmwithout MCS 0.1mmwithout MCS 0.01mmwithout MCS 0.001mm

NIST CSDARange

From Tatsumi Koi

Geant4 Workshop, Lisbon 9-14 October 2006 12

Cuts-value dependance ?Hadron therapy using protons for cancer treatment requests better than 1% agreement with measurements and ICRU/NIST protocol data.We had reported a proton range shift problem in water about 1 year before. i.e. the range of 200 MeV proton become longer about 3 mm than NIST range by applying a longer production cut.

200MeV Proton, ICRU predicts259.6mm

G4hLowEnergyIonisationNo ChemicalFormulaNuclearStoppingOff

500um100um50um10um5um3um1um

Sur

vive

d pr

oton

pro

babi

lity

Depth in Water ( mm )

Production Cut

From Tsukasa Aso

not coherent with previous slide

Geant4 Workshop, Lisbon 9-14 October 2006 13

proton 100 MeV in water : cut saga

Proj. range standard lowE

cut 1 km 77.13 mm 76.29 mm

cut 15 um(~10 keV e-)

76.82 mm 77.30 mm

- 0.4 % + 1.3 %

nist : 77.07 mm - 0.3 % + 0.3 %

15 um-1km1km

by chance ?time: lowE/stand ~ 2

Geant4 Workshop, Lisbon 9-14 October 2006 14

Projected range : cut 15 um / infinite

Geant4 Workshop, Lisbon 9-14 October 2006 15

Projected range : Geant4 / Nist

Geant4 Workshop, Lisbon 9-14 October 2006 16

proton range in water - summary

In csda condition, lowE is off by 1% for all energies above ~ 20 MeVIt is at least 10 time slower than stand, due to an excessive step limitationProton range varies with production threshold

within 1% for stand1-2% for lowE

With low cut, both agree with nist values at all energies above 20 MeV, within 0.5%Then, lowE is ‘only’ ~2 time slower than stand

G4hLowEnergyIonisation (lowE) versus G4hIonisation (stand)