AGS CNI Update:Non-linear Corrections to

Energy Loss in Si Dead Layer

Outline

• Standard dead layer fitting technique

• Non-linear corrections

• Compare results of the two methods

Calculating Energy Loss• Generate dE/dx as a function of carbon energy (Ekin)

from MSTAR ver 2.00

• Calculate energy loss tables for 150 < Ekin < 2000 keV for dead layer thicknesses 20 < tdead < 100 g/cm2

Carbon Energy (keV)

dE/d

x (k

eV c

m2 /g

)

Standard Technique

• Fit linear correlation b/w Ekin and Edep for 400 < Ekin < 800 keV

Ekin = A + B Edep

B 1 A Edead

• Fit Slope (B) as linear function of Edead (A)

Slope = a + b Edead

Ekin = Edead + (a + b Edead) Edep

Edep

Eki

n

Non-Linear Corrections• Fit Ekin to Edep correlation for different tdead

Ekin = P0 + P1 Edep + P2 (Edep)2 + P3 (Edep)3 + P4 (Edep)4

Pn(tdead) depend on dead layer thickness

• Fit Pn(tdead) with 3rd order polynomial

Pn(tdead) = Cn,0 + Cn,1tdead + Cn,2(tdead)2 + Cn,3(tdead)3

• Now have 20 parameters rather than 2

Non-Linear Correction ResultsExtract T0 and tdead (Edead)From TOF to Ekin correlation

First data set

• March 13 – standard fit– Edead = 70.6 keV

tdead 21 g/cm2

– T0 = 27.7 ns

• March 23 – non-linear fit– tdead = 34.2 g/cm2

– T0 = 26.4 ns

Second data set

• April 1 – standard fit– Edead = 63.4 keV tdead 19 g/cm2

– T0 = 34.4 ns

• April 1 – non-linear fit– tdead = 31.2 g/cm2

– T0 = 34.5 ns

Correction Effect on Polarization

First data set• March 13 – standard fit

<AN> = 1.28%

• March 23 – non-linear fit

<AN> = 1.26%

Second data set• April 1 – standard fit

<AN> = 1.29%

• April 1 – non-linear fit

<AN> = 1.28%

(Pnon-linear – Pstandard) / Pstandard

April 1 data