HITS510 Digitisation for drift chambers

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

RADD

( REAL) radius of cylindrical chamber in cm;

ZMIN

( REAL) z of lower end of cylindrical chamber;

ZMAX

( REAL) z of upper end of cylindrical chamber;

DETREP

( REAL) array of 8 with detector description:

1

number of wires;

2

wire spacing in $\phi$ (radians);

3

cosine of wire angle with respect to the z axis;

4

sine of wire angle with respect to the z axis (signed like $d\phi /dz$ );

5

$d\phi /dz$ along wire;

6

$\phi$ of point with z=0 on wire 1;

7

drift velocity (cm $nsec-1$ );

8

if >0 user routine GUDTIM will be called to calculate drift time;

HITREP

( REAL) array of 4 describing the track:

1

$\phi$ coordinate of intersection;

2

z coordinate of intersection;

3

$d\phi /dr$ ;

4

$dz/dr$ ;

IOUT

( INTEGER) array of 4 with digitisation information:

1

wire number (1... NWI with increasing phi), -1 if DETREP parameters are inconsistent;

2

drift time in nsec, >0 if $\phi (hit)>\phi (wire)$ ;

3

digitised current division information (relative position of charge along wire, per mille);

4

amount of charge deposited onto wire.

                        Charge                     
         .              |                        .
         |              .                        |
         =========================================  SENSE WIRE
     ...................................................> Z (cm)
         Z              Z                        Z 
          l                                       u
     ...............................................> ICD (0<ICD<1000)
         0              ICD                      1000
               ICD                (1000-ICD)

Figure: Coordinate system along the wire

Knowing the position Z of the deposit of charge we can calculate

$ICD=\; L\; \{Z-Z$_lZ_u-Z_l}

where L=1000 in the program. This is the information stored into IOUT(3).

CALL GCDERR (ICD*,ERP,ERS)

ICD

( INTEGER) digitised current division information ($\le ICD\le 1000$ ), overwritten on output with the modified value taking into account the errors;

ERP

( REAL) variance of Gaussian pedestal errors on the measured pulse heights relative to the sum of the pulse heights;

ERS

( REAL) variance of Gaussian slope errors on the measured pulse heights relative to the each pulse heights.

$ICD=\; L\; \hspace{1em}\{I$₂I₊}&sp;with&sp;I₊= I₁+I₂

Its error is determined by:

$\delta ICD=\; -\; \{ICDI$₊}δI₁+ {L-ICDI₊}δI₂&sp;and&sp;δI₁= δ₁+ ε₁ I₁&sp;;&sp;δI₂= δ₂+ ε₂ I₂

$\delta$₁ and $\delta$₂ are of dimension [I] and represent the pedestal errors. $\epsilon$₁ and $\epsilon$₂ are the slope errors. Errors are independent (no correlations), with a Gaussian distribution with average 0 and ERP as relative variance for pedestals $\delta$_i/I₊

and ERS as variance for slopes $\epsilon$_i . This gives the final result

$\delta ICD=\; -\{\delta$₁I₊}ICD+ {δ₂I₊}(L-ICD)_pedestals+ (ε₂-ε₁){ICD(L-ICD)L}_slope

GCDERR sets the ICD obtained from GCDRIF to $ICD=ICD+\delta ICD$ with $0\; \le ICD\le L$ .

GUDTIMVALUE = GUDTIM(DETREP,HITREP,IW1,DIS) The arguments have the same meaning than for GCDRIF apart from:

IW1

( INTEGER) wire number which will generate a signal;

DIS

( REAL) distance from the track to the wire;

R.Brun

IOPA001