MM's    Gen-Tracking Programs  Version II

The programs, written entirely in FORTRAN 77 are developed under Digital Unix Version 4 and should run as well on Solaris, HP/UX and Linux.
 

Contents

 
The Reconstruction

The Coordinate System
The Vertical Offset
The Target Magnetic Field

The Target Tracking
The HMS Tracking
The Gen Tracking

TARGETHMSELECTRONVIRTUALMATRIX
RECON
RECONX
RECONG
VIEW
Making the Programs
Data Files Needed
Event Data nTuple Contents
Other Files You May Be Interested In

The Reconstruction

In order to use still the knowledge on HMS accumulated so far at JLAB we decided to separate the two problems:

The Coordinate System
The reconstruction uses three different coordinate systems - the focal plane coordinates, the target coordinates and the beam coordinates, all of them right handed:
 

Length is measured in [cm] (module trg_track) or in [m] (modules hms_track and gen_track).
 
The Vertical Offset
From the focal plane quantities (x, x', y, y') measured by HMS a vertical beam offset can not distinguished from an offset in the electrons energy. A beam offset of 1cm corresponds to a shift in energy of about 1%.

Therefore, the vertical beam offset has to be measured with some kind of a beam monitor. The value measured is used to correct the measured focal plane quantities. This allows to use the standard reconstruction function optimized for the case where no vertical offest is present.
 

Treating the Vertical Beam Offset

Step	Description
1	Apply the standard reconstruction function R to the measured focal plane quantities (x,x',y,y') to get a first estimate for the target coordinates   (X=0,X',Y,Y',delta)i=1  = R(x,x',y,y')
2	Apply the forward transport function T to the estimated target coordinates for both X=0 and X = XBeam  to find the deviation of the focal plane coordinateds (dx,dx',dy,dy') caused by the vertical beam offset XBeam:  (dx,dx',dy,dy')i = T(X=X0,X',Y,Y',delta)i - T(X=0,X',Y,Y',delta)i  with X0=XBeam-ZX' (minor correction due to the Z coordinate of the intersection point)
3	Apply the standart reconstruction function R to the corrected focal plane quantities (x-dxi,x'-dxi',y-dyi,y'-dyi') to get a better estimate for the target coordinates  (X=0,X',Y,Y',delta)i+1  = R(x-dxi,x'-dxi',y-dyi,y'-dyi')
4	Goto step #2 until the change in delta is smaller than a given epsilon   | deltai - deltai+1| < epsilon

This iteration procedure is refered as reconstruction function V(x,x',y,y',X₀) in further sections.

The Target Magnetic Field
As the target magnetic field bends the electron track down (approx 1^o) the real vertical beam offset X_Beam-ZX' and the virtual beam offset X₀ (no target field) used in the procedure described above  differ by about 1mm (corresponding to a shift in energy of about 0.1%).

Therefore we designed an iterative procedure to find the virtual beam offset X₀. in presence of the magnetic field. With this knowledge we preform a reconstroction by appling the function V (this includes the beam offset)  to the focal plane coordinates and to the target coordinates. This coordinates describe the track of the electron outside HMS. As V does not include the target field this track is only valid as long as the electron stays in the field free region. To
include the effects of the field we track the particle from the field free region
back into the target field to the intersection with the incident beam.
 

Treating the Target Magnetic Field

Step	Description
1	Apply the reconstruction function V to the measured quantities (x,x',y,y',X0,i=1=XBeam) to get a first estimate for the virtual target coordinates   (X=X0,i=1,X',Y,Y',delta)V,i=1  = V(x,x',y,y',X0,i=1=XBeam)
2	Track the electron from the field free region (e.g. Z=1m) back into the magnetic field to the intersection point with the incident beam to get a first estimate for the real target coordinates  (X,X',Y,Y',Z,delta)i=1  = T(X-X'Z,X',Y-Y'Z,Y',Z,delta)V,i=1
3	Find a better estimate for the virtual beam offset  X0,i+1 = (XBeam - (Xi -XBeam))-ZiXi'  = (2XBeam - Xi) -ZiXi
4	Apply the reconstruction function V to the measured (corrected) quantities (x,x',y,y',X0,i) to get a better estimate for the virtual target coordinates   (X=X0,i+1,X',Y,Y',delta)V,i+1  = V(x,x',y,y',X0,i+1)
5	Track the electron from the field free region (e.g. Z=1m) back into the magnetic field to the intersection point with the incident beam to get a better estimate for the real target coordinates  (X,X',Y,Y',Z,delta)i+1  = T(X-X'Z,X',Y-Y'Z,Y',Z,delta)V,i+1
6	Goto step #3 until Xi+1 is equal to the vertical beam offset   | Xi+1 - XBeam| < epsilon

 

The Program Modules

The Gen Electron arm package consists of the three main tracking modules "trg_track",
"hms_track" and "gen_track", the single value decomposition fit module and the
programs itself.

The Target Tracking
The target tracking module "trg_track" solves the differential equations of motion for a
charged particle in the target magnetic field via the 4th order runge kutta methode.

The module provides the following subroutines:

subroutine trgInit (map,theta,phi)

subroutine trgTrack (u,E,dl,l)

subroutine trgXTrack (u,E,dl,l,Bdl,xfunc,id)

subroutine trgTrackToPlane (u,E,dl,a,b,c,d)
 

map	char	I	name of the oxford field map (or empty = uniform field)
theta	real	I	orientation of the field axis (inplane angle) [deg]
phi	real	I	orientation of the field axis (out of plane angle; always = 0) [deg]
u	real(6)	IO	particle coordinates  u(1,2,3) x,y,z [cm] u(4,5,6) dx/dt,dy/dt,dz/dt [cm/ns]
E	real	I	particle energy * unit charge (<0 for electrons) [MeV]
dl	real	I	step size (<0 = time reversal) [cm]
l	real	I	tracking distance [cm]
Bdl	real	O	integrated Bxdl
xfunc	ext int	I	external interger function called once per iteration step defined as  integer function xfunc (id,t,l,u)  id int I track id t real I time of flight [ns] l real I path length [cm] u real(6) I particle coordinates (see above)
id	int	I	first argument passed to xfunc
a,b,c,d	real	I	parameter for the intersection plane (ax+by+cz+d=0)

 
trgInit initializes (loads) the target field map.

trgTrack tracks a single particle with given start coordinates u over the distance l.

trgXTrack tracks a single particle with given start coordinates u over the distance l.
and stores the track in a PAW/hbook ntuple.

trgTrackToPlane tracks a single particle with given start parameters and finds the
intersection of the particle track with a given plane.
 

Before calling trgTrack, trgXTrack or trgTrackToPlane the target field map has to be loaded by a call to trgInit.

The module provides the following subroutines:

subroutine hmsInitForward (map,order,path,p0)

subroutine hmsForward (uT,zT,u,z,lost)

subroutine hmsAccept  (uT,zT,u,z,lost)

subroutine hmsInitRecon (map)

subroutine hmsReconInPlane (u,uT)

subroutine hmsReconOutOfPlane (u,x,uT)
 

map	char	I	name of the forward or backward transport map
order	int	I	maximal order to take into account
path	bool	I	set to .true. in order to calculate the path length/TOF variation
p0	real	I	central momentum of HMS
uT  zT	real(6)  real	I  I	target coordinates:  uT(1,2) x [m],  dx/dz  = out of plane coordinate (downwards)  uT(3,4) y [m],  dy/dz  = in plane coordinate (_|_ on x,z)  uT(5) l [?] = pathlength deviation (?)  uT(6) delta = relative deviation of the particle  momentum from the central momentum  zT z [m]; in axis coordinate (towards HMS)
u  z	real(6)  z	O  O	focal plane coordinates:  u(1,2) x [m],  dx/dz  = out of plane coordinate (downwards)  u(3,4) y [m],  dy/dz  = in plane coordinate (_|_ on x,z)  u(5) l [?] = pathlength deviation (?)  u(6) delta = relative deviation of the particle  momentum from the central momentum  z z [m]; in axis coordinate (towards HMS)  (position where the particle stops inside HMS)
lost	bool	O	set to .true. if the particle is lost in the HMS, otherwise .false.
u	real(4)	I	focal plane coordinates (reconstruction only):  u(1,2) x [m],  dx/dz  = out of plane coordinate (downwards)  u(3,4) y [m],  dy/dz  = in plane coordinate (_|_ on x,z)
x	real	I	vertical beam offset at the target [m] (z=0)  (out of plane; downwards)
uT	real(6)	O	target coordinates (reconstruction only):  u(1,2) x [m],  dx/dz  = out of plane coordinate (downwards)  u(3,4) y [m],  dy/dz  = in plane coordinate (_|_ on x,z)  u(5) z [m] = in axis coordinate (towards HMS)  u(6) delta = relative deviation of the particle  momentum from the central momentum

hmsForward applies a single step cosy coordinate to find the focal plane coordinates (without treating the acceptance)

hmsAccept makes a multi step transport calculation in order to get  the acceptance

hmsInitRecon initializes (loads) the reconstruction map

hmsReconInPlane reconstructs the target coordinates  (delta, dx/dz, y, dy/dz) at z=0

hmsReconOutOfPlane reconstructs the target coordinates (delta, dx/dz, y, dy/dz) at z=0
including the effects of a given vertical beam offset
 

		Before calling hmsForward or hmsAccept the forward  transport maps have to be loaded by a call to hmsInitForward.
		Before calling hmsReconInPlane or hmsReconOutOfPlaneAccept the reconstruction map has to be loaded by a call to hmsInitRecon.
		Before calling hmsReconOutOfPlane the forward transport maps have to be loaded by a call to hmsInitForward.

The module provides the following subroutines:

subroutine genInitRecon (recon,field,thetaB,cosy,order,thetaE,p0)

subroutine genRecon  (u,x,y,uT)
 

recon	char	I	name of the forward or backward transport map
field	char	I	name of the Oxford field map
thetaB	real	I	orientation of the field axis (inplane angle) [deg]
cosy	char	I	name of the forward transport maps
order	int	I	maximal order to take into account
thetaE	real	I	spectrometer angle (in plane) [deg]
p0	real	I	central momentum of HMS
u	real(4)	I	focal plane coordinates:  u(1,2) x [m],  dx/dz  = out of plane coordinate (downwards)  u(3,4) y [m],  dy/dz  = in plane coordinate (_|_ on x,z)
x	real	I	vertical beam offset [m] (out of plane coord.; downwards)
y	real	I	horizontal beam offset [m] (inplane coord.; _|_ on xbeam, zbeam)
uT	real(6)	O	target coordinates:  u(1,2) x [m],  dx/dz  = out of plane coordinate (downwards)  u(3,4) y [m],  dy/dz  = in plane coordinate (_|_ on x,z)  u(5) z [m] = in axis coordinate (towards HMS)  u(6) delta = relative deviation of the particle  momentum from the central momentum

genRecon reconstructs the target coordinates (delta, dx/dz, y, dy/dz) including the effects of the targetr magnetic field and the vertical beam offset
 

Before calling genRecon the target field map, the forward and backward maps have to be loaded by a call to genInitRecon.

The Ready to Use Programs

A summary of the first results can be viewed in the picture gallery.
 
TARGET: (target.f, trg_track.f, CERNLIB)
tracking program - used to calculate electron/proton tracks within the target.

• solves the the differential motion describing the particle motion in a magnetic field (4th order runge kutta)
• the tracks are stored in a HBOOK/nTuple file

 

• to get the acceptance it goes step by step through the elements of HMS
• to get the focal plane coordinates (of the electrons going through) it makes it in one step through HMS
• stores the resulting event data in a HBOOK/nTuple file

1:	histogram with the input conditions
10:	nTuple with all lost electrons (initial, focal coordinates)
20:	nTuple with the detected ones (initial, focal coordinates)

 
 

• transports the electron through the target field (cf. TARGET)
• to get the acceptance it goes step by step through the elements of HMS
• to get the focal plane coordinates (of the electrons going through) it makes it in one step through HMS
• stores the resulting event data in a HBOOK/nTuple file

1:	histogram with the input conditions
10:	nTuple with all lost electrons (initial, focal coordinates)
20:	nTuple with the detected ones (initial, focal coordinates)

 
 

• transports the electron through the target field (cf. TARGET)
• to get the acceptance it goes step by step through the elements of HMS
• stores the resulting event data in a HBOOK/nTuple file

1:	histogram with the input conditions
10:	nTuple with all lost electrons (initial, focal coordinates)
20:	nTuple with the detected ones (initial, focal coordinates)

 
 
 

• reads the HBOOK/nTuple file with the event data  (written by ELECTRON)
• fits the reconstruction matrix (using the single value decomposition algorithm)
• stores the reconstruction matrix and the errors of the coefficients found in COSY format

• reads the HBOOK/nTuple file with the event data  (written by HMS)
• reads the reconstruction matrix (calculated by MATRIX)
• performs the reconstruction
• stores the results in a new HBOOK/nTuple file

1:	histogram with the input conditions
30:	nTuple with all lost electrons (initial, focal coordinates)
20:	nTuple with the result of the reconstruction  (initial, focal and reconstructed coordinates)

 
 

• reads the HBOOK/nTuple file with the event data  (written by HMS)
• reads the reconstruction matrix (calculated by MATRIX)
• reads the forward transport matrix
• performs the reconstruction
• stores the results in a new HBOOK/nTuple file

1:	histogram with the input conditions
30:	nTuple with all lost electrons (initial, focal coordinates)
20:	nTuple with the result of the reconstruction  (initial, focal and reconstructed coordinates)

 

• reads the HBOOK/nTuple file with the event data  (written by ELECTRON)
• reads the reconstruction matrix (calculated by MATRIX)
• reads the forward transport matrix
• reads the target field map
• performs the reconstruction
• stores the results in a new HBOOK/nTuple file

1:	histogram with the input conditions
30:	nTuple with all lost electrons (initial, focal coordinates)
20:	nTuple with the result of the reconstruction  (initial, focal and reconstructed coordinates)

 

• reads the reconstruction matrix (calculated by MATRIX)

 
• creates a HBOOK file with the matrix coefficients stored in 2-dim histograms for later visualization

1:	weight factors for the coefficients (calculated by powering the max. values of the focal plane coordinates with the corresponding exponents
10:	coefficients for the delta reconstruction
20:	coefficients for the dx/dz reconstruction
30:	coefficients for the y reconstruction
40:	coefficients for the dy/dz reconstruction

 

field_map.dat	target field map
fwd_maps.dat	forward matrix elements
bwd_map.dat	original backward matrix elements

 

x0,y0,z0,dx0/dz,dy0/dz,delta0	phase space coordinates at the target
x,y,dx/dz,dy/dz	focal plane coordinates
z	z-coordinate where the particle stops or 0 if it is detected
x1,y1,z1,dx1/dz,dy1/dz,delta1	reconstructed target coordinates

 

view_rc.kumac	kumac for viewing the reconstruction results
view_map.kumac	kumac for visualizing a reconstruction matrix
cmp_map.kumac	kumac for visualizing a reconstruction matrix
gen_prog.tar	all the files mentioned above packed into a tar archive