Run plan optimization for E99-117

We use Whitlow's fit plus elastic tail predicted by rosetail as the estimated $e^-$ cross section. For details of the run plan optimization algorithm please refer to

'E94-010 simulation and run plan optimization' by A.Deur, 09/08/1998

the postscript file is available at http://www.jlab.org/ xiaochao/testrun/opt.ps

We use average beam current 15$\mu A$, polarization 80%; target polarization 40%; spectrometer momentum acceptance $\Delta p = p \times \pm 4.0\%$ and solid angle acceptance 3.9 msr.



Kinematics: Beam energy = 5.7 GeV, $\theta_e=45^O$, 40cm $^3He$ target

$p_e$	$\nu$	$Q^2$	x	$\Delta p$	$\epsilon$	W
(GeV/c)	(GeV)	(GeV$^2$)		(GeV/c)		(GeV/c$^2$)
1.45	4.25	4.858	0.61	0.116	0.3823	3.985
1.20	4.50	4.007	0.48	0.096	0.3250	5.315
0.89	4.81	2.972	0.33	0.072	0.2491	6.932

$p_e$	$\alpha$	$\beta$	Whitlow	rosetail	$\big(\frac{\mathrm{d}^2\sigma}{\mathrm{d}\Omega\mathrm{d}E'}\big)_{e^-}$	rates (Whitlow)
(GeV/c)			(nb/GeV-sr)	(nb/GeV-sr)	(nb/GeV-sr)	(s$^{-1}$)
1.45	2.5554	0.5628	1.0429	0.011	1.054	0.1569
1.20	2.7521	0.4814	2.2178	0.034	2.252	0.2752
0.89	3.0118	0.3738	4.3297	0.151	4.481	0.3985

The total beam time is about 20 days, then

$p_e$	t$_{\parallel}$	t$_{\perp}$	N$_{\parallel}$	N$_{\perp}$	$\Delta A_1^{^3 He}$	$\Delta A_1^{n}$
(GeV/c)	(hours)	(hours)			(f = 0.95)
1.45	189.36	41.71	106975	23562	2.84%
1.20	120.58	21.09	119469	20895	2.84%
0.89	95.42	11.84	136890	16990	2.84%

$\bigstar$ The error of asymmetry is $\Delta A_1^{^3 He}=0.863\%/(0.8*0.4*0.95)=2.84\%$;
$\bigstar$ The radiation length for 25 cm $^3$He target is:
before interaction:
10 mil Be + 10 mil Al + 0.012 mm Pyrex
+ 20 cm Air + 25 cm/2 $^3$He (10atm) = 0.3574%
after interaction:
25 cm/2 $^3$He (10atm) + 10 mil Al + 1.4 mm Pyrex
+ 20 cm Air + 7 mil Kapton + 4 mil Ti = 1.673%
$\bigstar$ Total cross section is estimated by the sum of Whitlow's fit and elastic tail given by rosetail.f, but only Whitlow's cross section is used for estimating the statistical error and optimize the run plan.