class THaOpticsAnalytical: public THaOptics

    THaOpticsAnalytical



 Author: Jin Huang <mailto:jinhuang@jlab.org>    Feb 2008
    Modify History:

What's this?

THaOpticsAnalytical is a derived class of THaOptics, which uses a analytical approach calculating track back to target for BigBite spectrometer. One can mount it to a THaOptics-supporting spectrometer by following line and fill up database according to last section.

Bool_t mr=MountOptics(new THaOpticsAnalytical("opticstest","BigBite Optics",this));
assert(mr);

Feature of the model

Since the solid angle of bigbite is relatively large, it will not be possible to use a single matrix to describe backward optics calculation for this spectrometer. This is because for backward matrix, it will be deeply involved with parameters such as distance between magnetic and target. This dependancy is not simple and a matrix for one experiment will not be able to be used on the other. Besides, the angle of spectrometer will also affect the matrix element. The overall error of matrix methord is equivalent to the spacial resolusion of detector is worth by the following amount :

$$\Delta x_{error}=\tan( \theta_{Target} )(\Delta L+\cos(\Theta_0)z_{react})$$

To solve these problem, a general, fitting free model is developped.

Assumption

This class use a analytical model calculating the whole track back to target given infomation of the track on the detector side. It based on the following assumption:

• The edge of magnetic field is sharp
• In the magnetic region, field is homogeneous and along y axis
• the front end of the magnetic field is along a surface perpendicular to central optics line
• The back end of magnetic field is along a surface, which could be described by a rotation of the front surface for a certain angle (described by fMagTheta) along y axis. The hight of the rotating axis is described by fMagS

Advantages over Matrix expansion

• No fitting needed. All input parameter is directly related to experiment setup.
• do not require condition, such as the particle is close to central optical axis.

thus, this optics class will be suitable for online replay, in which case, usually optics data is not available.

Beyond this model

accuracy of this model will not meet the requirement of further offline analysis. Therefore, the following steps is suggested for improvement of precision:

• Use otptical run data to build a correctiong table. And make an additional corrections base one this table in data analysis.
• Use otptical run data to fit a series of matrix element, and use THaOpticsHRS reading in the matrix and performing the optics calculation.

Algorithm Description

calculate bending radius

Base on the assumptions, a particle going through the whole system could be devided into 3 stages: drift in the target region, helix movement in magnetic feild and free drift in detector region. Following is a figure of a typical track, projected to midplane:

This also shows the temporary coordinate system used in internal function THaOpticsAnalytical::CalxA and THaOpticsAnalytical::CalR. These two fucntion use infomation of track parameter on the detector side and aprox. beam position to calculate position of point A(enter point), B(exit point) and bending radius R. For the y position, which is perpendicular to midplane, this model first assume a simple reflectiong model (get FirstVertex) and then correct it with calculated particle path (and get SecendVertex). Aproximate beam position is also corrected according to y position.

scaling bending radius to momentum

P=q*B*R=K*I*R, in which,

•  P is calculated momentum
•  q is charge of the incoming particle
•  B is the magnetic field
•  R is bending radius
•  K is an constant related to the magnetic
•  I is the current in coil

 there are two method of scaling bending radius to momentum:

1.  given current I and constant K
2.  given radius of central momentum

 this class will try both of above method.  Priority of method 1 is higher.

 a K<=0 will a push this class to use method 2

Database

This class will acquire following information from database (in additional to general THaOptics). All length units are meter and angle are degrees.

From db_run.dat

• <Spectrometer Name>.theta:Angle of Spectrometer.
• <Spectrometer Name>.pcentral:Central momentum. The final momentum will be scaled respect to this value
• <Spectrometer Name>.colldist:distance of sieve plane away from target center. As expressed as "L" in last section.

From db_<Spectrometer Name>.<Optics Module Name>.dat

• MagneticFieldFrontShift: distance between sieve plane and front boundary of magnetic field. Called "fMagDL" in code and picture above.
• MagneticFieldTopCrossing:Called "fMagS" in code and picture above.
• MagneticFieldRearSlopeAngle:Called "fMagTheta" in code and picture above.
• CurveRadiusOfCentralMomentum:For the central momentum, it will curve this given radius in the magnetic field. If it's an negative value, the code will automatically generate one according to definition.
• K:onstant K here, as discussed above. units: GeV/A/m/c