Log entry time 15:40:27 on July10,2004

Entry number 128122

It appears necessary to run with a significant PITA slope in order to 
zero a significant effect from the vacuum window birefringence.  The use 
of PITA offsets to zero charge asymmetry also easily zeros the position 
differences for appropriately chosen waveplate angles.  Steering
(or some other non-RHWP, non-IHWP modulated effect) is a non-negligible
component for y position differences, so these position differences are 
less easy to reduce.  These effects are several factors smaller than those
observed on Gun 3. 

Run conditions were found which allow a reasonable PITA offset to zero 
charge asymmetry while providing small position differences.  The x position
differences are generally seen to be <300 nm magnitude for both IHWP states.
The y position differences are seen as large as 1 micron, but do not flip sign
with IHWP (and so should cancel well). 

Injector transmission is an important issue, in that position differences
and charge asymmetry is clearly modified late in the injector.  If we
can demonstrate a stable (and desirable) behaviour of the beam off
the cathode, then reduction of helicity-correlated clipping in the injector
will become a priority.

The laser was very noisy.  It was nominally locked, but the phase noise 
readback was often ">5 ps".  The intensity jitter appeared to be at the 
5% level, with long tails on the charge asymmetry (and a charge asymmetry 
width of >2000 ppm, compared to <400 ppm for the comparable Hall C laser).
It is not clear that immediate corrective action is necessary, but
the extreme charge asymmetry tails are undesirable.



********************************************************************************
*
Discussion: sources of position differences and interpretation  of the RHWP 
scans 
********************************************************************************
*

Run  IHWP  Delta V
--------------------
2742  OUT      0
2744  OUT   -200
2747   IN      0
2749   IN   -200

Each RHWP scan was fit to the standard constant+(2*theta)+(4*theta) function.

A constant term in charge asymmetry (magnitude about 1880 ppm) 
flips very well between runs 2742 and 2747.  This strongly suggests a 
significant vacuum window birefringence, and prevents us from running with
a very small PITA slope (we need to have enough PITA slope to zero
this large offset).

The 2*theta term (magnitude around 880 ppm) in charge asymmetry flips very well 
between run 2742 and 2747, which suggests that the RHWP birefringence error
or analyzing power accounts for all of this effect.  The large DoLP introduced 
in runs 2744 and 2749 change this term by only about 10%, suggesting that the
2*theta term is dominated by a small deviation of the RHWP from half-wave
retardation for the Hall A  851 nm laser.  

There are 2*theta position difference amplitudes, also associated with 
the RHWP birefringence, which can be as large as 1 micron (comparable 
to the 4*theta position difference term).  These flip sign with the IHWP.

The 4*theta charge asymmetry terms in Runs 2742 and 2747 are <10%  
different in magnitude, with opposite signs (about 700 ppm).  This suggests
that we have a good Pockels cell voltage/tune for each IHWP state. 
The magnitude of the 4*theta term is approx. 11000 ppm for the -200 V
offset runs.  

The 4*theta terms for both x and y position differences change sign, with
magnitude changes generally less than factors of two.  This is consistent
with effects from Pockels cell birefringence gradients, upstream 
polarization gradients, and even analyzing power gradients.  These amplitudes
are not large, generally <.5 micron for IHWP OUT and <1 micron for IHWP IN.

There are enormous 4*theta amplitudes in both x and y position differences
for the Delta=-200V runs (as large as 15 um).  This is very suggestive
of a strong analyzing power gradient, probably on the cathode.  By way of
comparison, these 4*theta amplitudes were less than 1 micron on gun 3.

A significant constant term in x position differences can be attributed
to the birefringence in the vacuum window (suggested above) interacting with 
the cathode analyzing power gradient.  The magnitudes of the constant 
x position difference terms are consistent with the magnitudes of
the 4*theta terms in runs 2744 and 2749, when scaled by the ratios of
constant vs 4*theta charge asymmetry amplitudes.  These constant position
difference terms flip sign very closely with IHWP insertion (as expected).

The constant terms in the y-position differences are less easily understood.
There is a change in sign of the constant term between the two IHWP states
for some, but not all, of the bpms.  We cannot understand why the sign flip 
behaviour should be inconsistent between bpms.  Is it a worrisome indicator
of some higher order effects?  The mechanisms suggested here are (as with
x pos difs) vacuum window bi-ref + cathode gradients (this would flip sign
with IHWP) and steering (which would not flip sign). 

In the end, it all works out.  It isn't difficult to find an RHWP position which
zeros position differences for X (and reduces them for Y) while allowing a
reasonable PITA voltage offset.  It turns out that RHWP=3650 (73 degrees) 
is pretty good for both the IHWP states.  This is possible in part because
of the quality of Pockels cell (Arwen). A worse Pockels cell would have larger
effects from birefringence gradients, which are unaffected by the PITA offset
voltage. (Such an effect can be tuned out with the RHWP, but the vacuum window 
prevents us from further reducing the PITA slope, so we'd be sunk without
Arwen).  We are also seeing very little steering in X (we tuned it out 
with our work in the tunnel).  It is unfortunate that we could not solve our
"polarization problem" in the tunnel that prevented us from removing the
steering in Y, but luckily we wisely settled into a safe spot which keeps the
total effect small (below 1 micron, compared to 3-5 microns on Gun 3). 

We are very optimistic about this configuration!