26.7 MHz cavity mechanical tuner requirements Page: 4 of 5
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at peak torque of 100 rad/sec and max. table speed of 160 mm/sec.
B) What is time required to reach maximum tuning rate (i.e., time between injection porch and
v=a*t, (3.6rad/sec)/(40180rad/sec2) = .OOlsec .. Negligible compared to power supply
IV) Transition Crossing
At transition the tuner is moving at an initial velocity of
(0.3kHz/sec)*(1/10kHz/mm)*(1/4mm/rev)*2ir = 0.047rad/sec. We will see shortly that this is
negligible compared to the result.
The detuning angle is given by
Af_= IfourierCoS4s R
equals + 660 Hz, positive below -yT,
negative above 'YT.
For zero beam loading the stable phase point 4 is
jumped in the low level electronics of the beam control
system and the tuner does nothing. For full beam loading
the tuner must swing through 2*Afrf or 2*660Hz = -
1320 Hz (negative since going from +660 to -660 Hz).
This corresponds to
1320Hz * 1 *27rad/rev=0.21rad
We wish to know the minimum time required for the
phase jump given the maximum speed of the table and
the maximum acceleration rate. Given the maximum
acceleration rate of 40180 rad/sec2 and the initial
velocity of 0.047rad/sec we can neglect the time required
to reverse direction (1psec). Solving for the time
required to cover half the angle
0.21rad = at
t = 2.3 msec. Checking that we do not exceed the maximum velocity v = at = 40,000rad/sece
* 2.3 msec = 92 rad/sec < 100 rad/sec maximum. Therefore minimum time required to switch
phase at transition is 2*2.3msec = 4.6msec. W. Pirkl2 has pointed out that the amplifier would
see a substantially lower transient current at the anode if one "decompensates" for beam loading
near transition, thus seeing an error of only Afr rather than 2Afrf.
V) Overall loop response
The beam requires a phase accuracy of 0.150 of the rf voltage to avoid emmittance blowup. The
fast rf feedback allows errors within the feedback loop to be reduced by a factor of 100, to 150.
T Vt C . e
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Rose, J. 26.7 MHz cavity mechanical tuner requirements, report, February 1, 1995; United States. (digital.library.unt.edu/ark:/67531/metadc869739/m1/4/: accessed April 22, 2018), University of North Texas Libraries, Digital Library, digital.library.unt.edu; crediting UNT Libraries Government Documents Department.