Physics and Engineering of Radiation Detection

3.7. Sources of Error in Gaseous Detectors 205

E_+ (volts)

0 5 10 15 20 25 30

E (volts)

50

100

150

200

250

Figure 3.7.2: Dependence of space charge induced electric

fieldE+insidea2cmlong parallel plate chamber on the

effective electric field intensity at three distances from the

anode: 2.5cm(dotted line), 3.5cm(dashed line), 4.99cm

(solid line). Applied voltage is 500V.

surviving the absorption after traveling a distancex.φ 0 is simply the incident photon
flux. The term on brackets represents the number of photons being absorbed per
unit time in a thicknessx′fromx.
Let us now suppose that the photon flux is constant in time. In this case the rate
of creation of charge pairs will also be constant. The charge pairs thus created will
move in opposite directions and constitute a current. The current can be integrated
over time to determine the total charge. A good approximation of the total charge
Qproduced by the movement of charges by a distance xis

Q=

eN

v

x (3.7.30)

whereNrepresents the number of charges each having a unit chargeeand moving
with a drift velocityv. Using the relation we can estimate amount of space charge
inthevolumeelementδxto be

Q=

eEγ

Wv+

e−μρx

∫h

y=0

∫b

z=0

φ 0 (y, z, t)dydz

∫x+δx

x′=x

(

1 −e−μρx

′)

dx′. (3.7.31)

Here