[Halld-cal] BCAL constants - veff and time-walk / thoughts on determination

[Elton Smith]

Collaborators,

I thought I should pass this on the mail list for future reference. We had a discussion last week regarding BCAL calibration tasks. We listed some of the
topics that need work:
https://halldweb1.jlab.org/wiki/index.php/Feb_4,_2015_BCAL_Commissioning#Action_Items
See also "Low-level calibration constants for BCAL"
(http://argus.phys.uregina.ca/cgi-bin/private/DocDB/ShowDocument?docid=2618)

Among these, we listed some that might be of interest/appropriate for George Vasileiadis and Christine has tentatively agreed that they can pursue these studies.
6 Determine effective velocity for each channel (George?)
7 Determine time-walk corrections (George?)
8 Determine time offsets (?)


v_eff (cm/ns) - Effective velocity of signal propagation inside the BCAL.
===========================================

Let t_u (ns) be the time measured by the upstream sensors
let t_d (ns) be the time measured by the downstream sensors

Let t_u^0 be the time measured by the upstream sensors for particles
hitting the center of the module
let t_d^0 be the time measured by the downstream sensors for particles
hitting the center of the module

Let z be the position (cm) of energy deposition in the module relative
the center of the module (z=0).

Then for energy deposited at position z, we get

t_u = t_u^0 + z/v_eff
t_d = t_d^0 - z/v_eff

Delta_t = t_u - t_d = (t_u^0-t_d^0) + 2z/v_eff

To determine v_eff, we need to know the position of energy deposition.
Use a sample of charged tracks incident on the BCAL and use the
reconstructed tracks in the CDC/FDC to determine the position of impact
on the BCAL, call this z_trk. Then the plot of Delta_t vs z_trk should
be a straight line with a slope alpha = 2/v_eff. The intercept (z=0)
determines the relative timing offsets between upstream and downstream,
i.e. t_u^0 - t_d^0. These determine are half of the time offsets in #8
above.

For this project we need a program that can track charged tracks to the
BCAL and identify corresponding energy depositions. One may wish to
start analyzing cosmic-ray data as they may provide the cleanest sample,
but improved timing efficiency and resolution may be achieved with
larger energy depositions.

Time-walk corrections for TDC data
======================
Refer to GlueX-doc-2618

We need to decide on the precise form of time-walk correction function
to use, but the process for extracting the parameters is independent on
the specific form used. My suggestion for the time-walk function is
given by (Eq. 5 and 6 in GlueX-doc-2618):

Let t^w be the walk-corrected time and t be time in ns adjusted for
constant offsets. Then

t^w = t - (f^w(a/T) - f^w(a0/T)), where

f^w(a) = c0 + c1/(a/T)^c2

T is the TDC threshold and a is the raw ADC pulse integral. c0, c1 and
c2 are the time-walk correction constants. Note that c0 might be useful
for various operations, but cancells in the correction itself. The
current form is setup so that there is no correction for a = a0. a0 is a
predetermined typical FADC value which we choose so that the time-walk
correction is zero.

We do not expect any time-walk for the times coming from the FADC
(t_adc). Therefore, we would expect that t_adc ~ t^w, where there may be
differences in resolution between the two quantities, but on average the
difference should yield the time-walk function as follows:

t - t_adc = (f^w(a/T) - f^w(a0/T))

Plotting this value as a function of the pulse integral a, one should be
able to fit for the constants c1 and c2. This study is perhaps more
straight-forward than the previous one and Mark has also done some
preliminary studies of the pulse height dependence on time.


-- 
Elton Smith
Jefferson Lab MS 12H3
12000 Jefferson Ave STE 4
Newport News, VA 23606
(757) 269-7625
(757) 269-6331 fax