Drift property in non-uniform B field.

T.Sawada

June 18, 2004

Electron drift in E and non-uniformed B field• Drift velocity of electron in E, B field (Langevin equation)

• First order Runge-Kutta integration was applied

collisionbetweentimemean

frequencycyclotron

mobility

BBEBEEE

vd

:

:

:

)ˆ)ˆˆ()(ˆˆ)(ˆ()(1

22

timeDriftT

positionfinalInitialrr

dtrvrr

steptrvr

fi

T

dif

d

:

)(:)(

)(

1:)(

0

0

0

Strategy of correction

1. Determine 　　　　　　　　 by the data of B=0 (vd=5cm/usec).

2. Execute Runge-Kutta intergration in non-uniform B

timedrift

dif dtrvrr

wirezofcoordinatez

planePadinyxyx

0

:0

:0,0

)(

,

)( mobility

Run # 28911 (CR) before correctionCut condition: chi2Pad > 0.02 , chi2Z > 0.02 , -0.4 < lambda (dip angle) <0.4

Layer-dependence of resZ

Layer

( at -1400 < z < -1300 )

resZ (m

m)

resZ (m

m)

Z-dependence of resZ

Z (mm)

Cut condition: chi2Pad > 0.02 , chi2Z > 0.02 , -0.4 < lambda (dip angle) <0.4

( -1400 < z < -1300 )Run # 28911 (CR) before correction

resZ (mm) resZ (mm)

Layer = 0 Layer = 1

Cut condition: chi2Pad > 0.02 , chi2Z > 0.02 , -0.4 < lambda (dip angle) <0.4

( -1400 < z < -1300 )Run # 28911 (CR) before correction

resZ (mm) resZ (mm)

Layer = 2 Layer = 3

Cut condition: chi2Pad > 0.02 , chi2Z > 0.02 , -0.4 < lambda (dip angle) <0.4

( -1400 < z < -1300 )Run # 28911 (CR) before correction

resZ (mm) resZ (mm)

Layer = 4 Layer = 5

Cut condition: chi2Pad > 0.02 , chi2Z > 0.02 , -0.4 < lambda (dip angle) <0.4

( -1400 < z < -1300 )Run # 28911 (CR) before correction

resZ (mm) resZ (mm)

Layer = 6 Layer = 7

Cut condition: chi2Pad > 0.02 , chi2Z > 0.02 , -0.4 < lambda (dip angle) <0.4

( -1400 < z < -1300 )Run # 28911 (CR) before correction

resZ (mm) resZ (mm)

Layer = 8 Layer = 9

Cut condition: chi2Pad > 0.02 , chi2Z > 0.02 , -0.4 < lambda (dip angle) <0.4

( -1400 < z < -1300 )Run # 28911 (CR) before correction

resZ (mm) resZ (mm)

Layer = 10 Layer = 11

Cut condition: chi2Pad > 0.02 , chi2Z > 0.02 , -0.4 < lambda (dip angle) <0.4

( -1400 < z < -1300 )Run # 28911 (CR) before correction

resZ (mm) resZ (mm)

Layer = 12 Layer = 13

Run # 28911 (CR) after correction

Z (mm)

resZ (m

m)

resZ (m

m)

Layer

( at -1400 < z < -1300 )

Cut condition: chi2Pad > 0.02 , chi2Z > 0.02 , -0.4 < lambda (dip angle) <0.4

Layer-dependence of resZ Z-dependence of resZ

resZ (mm) resZ (mm)

Layer = 0 Layer = 1

Run # 28911 (CR) after correction

Cut condition: chi2Pad > 0.02 , chi2Z > 0.02 , -0.4 < lambda (dip angle) <0.4

( -1400 < z < -1300 )

resZ (mm) resZ (mm)

Layer = 2 Layer = 3

Run # 28911 (CR) after correction( -1400 < z < -1300 )

Cut condition: chi2Pad > 0.02 , chi2Z > 0.02 , -0.4 < lambda (dip angle) <0.4

resZ (mm) resZ (mm)

Layer = 4 Layer = 5

Run # 28911 (CR) after correction( -1400 < z < -1300 )

Cut condition: chi2Pad > 0.02 , chi2Z > 0.02 , -0.4 < lambda (dip angle) <0.4

resZ (mm) resZ (mm)

Layer = 6 Layer = 7

Run # 28911 (CR) after correction( -1400 < z < -1300 )

Cut condition: chi2Pad > 0.02 , chi2Z > 0.02 , -0.4 < lambda (dip angle) <0.4

resZ (mm) resZ (mm)

Layer = 8 Layer = 9

Run # 28911 (CR) after correction( -1400 < z < -1300 )

Cut condition: chi2Pad > 0.02 , chi2Z > 0.02 , -0.4 < lambda (dip angle) <0.4

resZ (mm) resZ (mm)

Layer = 10 Layer = 11

Run # 28911 (CR) after correction( -1400 < z < -1300 )

Cut condition: chi2Pad > 0.02 , chi2Z > 0.02 , -0.4 < lambda (dip angle) <0.4

resZ (mm) resZ (mm)

Layer = 12 Layer = 13

Run # 28911 (CR) after correction( -1400 < z < -1300 )

Cut condition: chi2Pad > 0.02 , chi2Z > 0.02 , -0.4 < lambda (dip angle) <0.4

Summary• The Mean Value of the residual of Layer(5

～ 13) aprroached almost 0 !!

( Correction of Layer(0 ～ 1) is parhaps needed consideration of non-uniformity of the electronic field around Target-holder. )

• I intend to study the following in future :

　＞ improvement of resZ of Layer(0 ～ 4)

＞ Z-dependance of resZ.