Digitisation of Drift Chambers

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| Geant 3.10  |               GEANT User's Guide              | HITS510  ##
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Author(s) : W.Mitaroff                                 Submitted: 21.02.85
Origin    : Same                                         Revised: 22.04.86
                                  

  +--------------------------------------------------------------------+
  |CALL GCDRIF (RADD,ZMIN,ZMAX,DETREP,HITREP,IOUT*) |
  +--------------------------------------------------------------------+
                                  

Digitisation routine for a cylindrical drift chamber.

RADD

radius of cylinder in cm

ZMIN

z of lower end of cylinder

ZMAX

z of upper end of "

DETREP(1)

number of wires

DETREP(2)

wire spacing in PHI (radians)

DETREP(3)

cosine of wire angle

DETREP(4)

sine of wire angle (signed like dphi/dz)

DETREP(5)

dphi/dz along wire

DETREP(6)

phi of point with z=0 on wire 1

DETREP(7)

drift velocity (cm/nsec)

DETREP(8)

quantity describing the drift angle if.ne.0 ==> user routine GUDTIM

HITREP(1)

phi coordinate of intersection

HITREP(2)

z coordinate

HITREP(3)

dphi/dr

HITREP(4)

dz/dr

IOUT(1)

wire number (1..NWI with increasing phi) (-1 for bad DETREP parameters)

IOUT(2)

drift time (nsec) (+/- for phi(hit)>/< phi(wire)

IOUT(3)

digitised current division information (rel. pos. along wire of charge) (per mille)

IOUT(4)

amount of charge deposited to wire

Coordinate systems along wire

I_1                    Charge         I_2;
                                            SENSE WIRE
Z_L                   Z_0             Z_u                  Z(cm)
.                                                   X (arbitrary scale)
0                     X_0          (L-X_0)     L

The scaling used is such that L = 1000.

Knowing the position Z of the deposit of charge, 0

X = L# ((Z -Z )/(Z -Z )) 0 0 L u L

This information is stored into IOUT(3).

             +----------------------------------------------+
             | CALL GCDERR (ICD,ERP,ERS) |
             +----------------------------------------------+
                                  

Routine to calculate the error on the current division information as obtained by GCDRIF.

ICD

digitized current division information (0... 1000)

ERP

variance of Gaussian distributed pedestral errors on the measured pulse heights relative to the sum of the pulse heights

ERS

variance of Gaussian distributed slope errors on the measured pulse heights relative to the each pulse heights

Here we assume that X has been determined by measuring the pulse heights 0 I ,I ; with some statistical errors. 1 2

X is then given by the formula 0

X = L# I /I withI =I +I 0 2 + + 1 2

and its error is determined by

deltaX =-(X /I )deltaI +(L-X / I )deltaI 0 0 + 1 0 + 2

with the errors on measuring the pulse heights

deltaI = delta + epsilon # I deltaI = delta +epsilon # I 1 1 1 1 2 2 2 2

delta delta are of dimension (I) and represent the "pedestal" errors; 1 2

epsilon ,epsilon are the "slope" errors. All are assumed to be 1 2 distributed |independently| (no correlations), randomly and Gaussian around zero. This gives the final result

    deltaX  =- ((delta )/(I ))X  +((delta )/ (I ))(L-X ) +(epsilon -epsilon )((X  (L-X ))/(L))
          0   ##################### ####################   ################# #################
             |####################{z###################}  |################{z################}
                             "pedestals"                                 "slope"

In GCDERR, the X derived from 0

GCDRIF is set to

X = X + deltaX (but 0<=X < =L) 0 0 0 0 using ERP ...variance for delta /I ,delta / I distributions 1 + 2 +

ERS ...variance for epsilon ,epsilon distributions. 1 2