Hi,
I worked this out awhile ago. If the data acquisition time is
T_live, the dead time (stop DAQ, ramp down, inject, ramp up start DAQ) is
T_dead, and the exponential decay of the beam intensity is tau then to
maximize the average luminosity you want to collect data for
T_live = SQRT( 2.0 * T_dead * tau )
Assuming T_dead = 2 min and tau = 16 minutes then T_live = 8 min whci
corresponds to the a beam intensity of 60% of the original intensity.
Not sure I agree with the table as it would indicate the best time to stop
is as soon as possible.
--On Monday, July 21, 2003 6:45 PM -0400 Aaron Joseph Maschinot
<ajmasch@MIT.EDU> wrote:
>
> in the interest of maximizing luminosity, the average beam current should
> be maximized. if one assumes an exponential beam current fall-off rate
> such as:
>
> I = I_0 * exp(-t/lambda)
>
> then it can be shown with some basic calculus that the average beam
> current is given by the following:
>
> I_avg = - lambda * exp(-t_hvup/lambda) * (I_stop - I_0)
> / [t_hvdown + t_fill + t_dead - lambda * ln(I_stop/I_0)]
>
> where:
>
> I_avg = average beam current
> I_stop = current you choose to stop the data-taking at
> I_0 = maximum beam current
> lambda = beam lifetime
> t_hvup = time to ramp up HV after injection maximum
> t_hvdown = time to ramp down HV before injection begins
> t_fill = time for current to go from 0 to beam current maximum
> t_dead = time after HV ramp down but before beam filling begins
>
> (i welcome someone to check this. note that the "exp(-t_hvup/lambda)"
> factor arises because we don't start taking data until the HV has ramped
> up AFTER the injection maximum is reached.)
>
> anyway, assuming the above equation is correct (or about so; i don't think
> we're quite ready to worry about lambda changing with run-time), i have
> calculated the beam current at which data taking should be stopped
> (I_stop) in order to maximize the average current. note that i assumed
> the following:
>
> t_hvup + thvdown + tfill = 2 minutes
>
> from my shift-taking experience, i know that this is a good estimate.
> these stop-current values are listed below as functions of I_0 and
> lambda, both of which will switch depending on the target, the beam
> behavior, a sneeze in japan.
>
> maybe, at the beginning of each shift, the shift-takers should do a few
> fills, find out what the beam maximum is for the night and get an estimate
> for lambda, and then set the fill current accordingly.
>
> i have taped a copy of the results below to one of the computers in the
> counting bay. if my calculations are wrong, tear it down; i don't care
> (personal pride was lost a long time ago).
>
> aaron
>
>
>
> Imax = maximum beam fill current (in mA)
> lamb = beam lifetime (in minutes)
> Istp = current to refill at in order to maximize average current (in mA)
> Iavg = average current if you refill at Iavg (in mA)
>
> -------------------------------------------------------------------------
> --
>
> Imax || lamb Istp Iavg | lamb Istp Iavg | lamb Istp Iavg | lamb Istp Iavg
> 70 || 10 42 40 | 12 44 42 | 14 46 44 | 16 47 45
> 75 || 10 45 43 | 12 47 45 | 14 49 47 | 16 50 49
> 80 || 10 48 46 | 12 50 48 | 14 52 50 | 16 53 52
> 85 || 10 51 49 | 12 54 51 | 14 55 53 | 16 57 55
> 90 || 10 54 52 | 12 57 54 | 14 59 57 | 16 60 58
> 95 || 10 58 55 | 12 60 57 | 14 62 60 | 16 63 61
> 100 || 10 61 58 | 12 63 60 | 14 65 63 | 16 67 65
> 105 || 10 64 60 | 12 66 63 | 14 68 66 | 16 70 68
> 110 || 10 67 63 | 12 69 67 | 14 72 69 | 16 73 71
> 115 || 10 70 66 | 12 72 70 | 14 75 72 | 16 77 74
> 120 || 10 73 69 | 12 76 73 | 14 78 75 | 16 80 78
> 125 || 10 76 72 | 12 79 76 | 14 81 78 | 16 83 81
> 130 || 10 79 75 | 12 82 79 | 14 85 82 | 16 87 84
> 135 || 10 82 78 | 12 85 82 | 14 88 85 | 16 90 87
> 140 || 10 85 81 | 12 88 85 | 14 91 88 | 16 93 91
> 145 || 10 88 83 | 12 91 88 | 14 94 91 | 16 97 94
>
> Imax || lamb Istp Iavg | lamb Istp Iavg | lamb Istp Iavg | lamb Istp Iavg
> 70 || 18 48 46 | 20 49 47 | 22 49 48 | 24 50 49
> 75 || 18 51 50 | 20 52 51 | 22 53 52 | 24 54 53
> 80 || 18 55 53 | 20 56 54 | 22 56 55 | 24 57 56
> 85 || 18 58 56 | 20 59 58 | 22 60 59 | 24 61 60
> 90 || 18 61 60 | 20 63 61 | 22 64 62 | 24 64 63
> 95 || 18 65 63 | 20 66 64 | 22 67 66 | 24 68 67
> 100 || 18 68 66 | 20 69 68 | 22 71 69 | 24 72 70
> 105 || 18 72 70 | 20 73 71 | 22 74 72 | 24 75 74
> 110 || 18 75 73 | 20 76 75 | 22 78 76 | 24 79 77
> 115 || 18 78 76 | 20 80 78 | 22 81 79 | 24 82 81
> 120 || 18 82 80 | 20 83 81 | 22 85 83 | 24 86 84
> 125 || 18 85 83 | 20 87 85 | 22 88 86 | 24 90 88
> 130 || 18 89 86 | 20 90 88 | 22 92 90 | 24 93 91
> 135 || 18 92 90 | 20 94 92 | 22 95 93 | 24 97 95
> 140 || 18 96 93 | 20 97 95 | 22 99 97 | 24 100 98
> 145 || 18 99 96 | 20 101 98 | 22 102 100 | 24 104 102
>
> Imax || lamb Istp Iavg | lamb Istp Iavg | lamb Istp Iavg | lamb Istp Iavg
> 70 || 26 51 50 | 28 51 50 | 30 52 51 | 32 52 51
> 75 || 26 54 53 | 28 55 54 | 30 56 55 | 32 56 55
> 80 || 26 58 57 | 28 59 58 | 30 59 58 | 32 60 59
> 85 || 26 62 60 | 28 62 61 | 30 63 62 | 32 64 63
> 90 || 26 65 64 | 28 66 65 | 30 67 66 | 32 67 66
> 95 || 26 69 68 | 28 70 68 | 30 70 69 | 32 71 70
> 100 || 26 73 71 | 28 73 72 | 30 74 73 | 32 75 74
> 105 || 26 76 75 | 28 77 76 | 30 78 76 | 32 78 77
> 110 || 26 80 78 | 28 81 79 | 30 81 80 | 32 82 81
> 115 || 26 83 82 | 28 84 83 | 30 85 84 | 32 86 85
> 120 || 26 87 85 | 28 88 86 | 30 89 87 | 32 90 88
> 125 || 26 91 89 | 28 92 90 | 30 93 91 | 32 93 92
> 130 || 26 94 92 | 28 95 94 | 30 96 95 | 32 97 96
> 135 || 26 98 96 | 28 99 97 | 30 100 98 | 32 101 99
> 140 || 26 102 100 | 28 103 101 | 30 104 102 | 32 105 103
> 145 || 26 105 103 | 28 106 104 | 30 107 106 | 32 108 107
>
>
>
Cheers,
Douglas
26-415 M.I.T. Tel: +1 617 258 7199
77 Massachusetts Avenue Fax: +1 617 258 5440
Cambridge, MA 02139, USA E-mail: hasell@mit.edu
This archive was generated by hypermail 2.1.2 : Mon Feb 24 2014 - 14:07:29 EST