26.7 MHz cavity mechanical tuner requirements Page: 3 of 5
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where L is the screw length, g gravitational constant, 'y is the density in g/cm3, d is the screw
radius in cm, and 1 is the lead of the screw in mm/revolution. For ease of calculations using the
motor data the inertia's are expressed in terms of the obscure units of kg-cm-sec2 by dividing
by the gravitational constant.
Motor (5.8X10 4) + Jscrew (7.9x10-6) + JIoad (5.6x10-5) =Jtoa = 6.4x10-4kg-cm-sec2.
Solving for the acceleration in the torque equation we arrive at the peak acceleration of 40,180
II) Required Accuracy
The beam must see phase errors of less than 0.15 degrees2 in order to keep emmittance
growth due to the errors below 1 %. The cavity will have local feedback closed around the tuning
loop which will have a gain of 100, this reduces the tolerance within the feedback to 15 degrees.
In this case the power amplifier must be able
to provide the additional power. At 15 off
the peak of the resonance the cavity voltage
drops by V=Vo cos 15, or 0.966Vo. Since
the power required goes as the square of the
voltage or .9662, P=1.07Po, which is well
within the reserve of the amplifier. In order
to give adequate margin for the design of the
tuner we will use a 7.50 accuracy
requirement for the subsequent calculations.
The 7.5* corresponds to a frequency
7.5 =tan-1( f2Q)
for a Sf of 117 Hz. In terms of a tuning
sensitivity of approximately 10 kHz/mm this corresponds to 117Hz/lOkHz/mm or 11.7 m. This
is well within the advertised accuracy of 2 m of the servo.
III) Tuner Performance
Tuner sensitivity varies between 14.6 and 10 kHz/mm, while the required dynamic tuning
range is 90 kHz + 30 kHz of slow tuning to compensate for thermal detuning. This is easily met
by less than 16mm of tuner travel, out of a possible 25mm.
The maximum tuning rate is given at the beginning of the acceleration cycle of gold and is
A) Check maximum tuning rate: 23kHz/sec at 10kHz/mm = 2.3mm/sec. Pitch is 4mm/rev:
(2.3mm/sec)/(4mm/rev)x27rrad/rev = 3.6rad/sec .. Much less than the maximum motor speed
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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/m1/3/: accessed January 23, 2019), University of North Texas Libraries, Digital Library, digital.library.unt.edu; crediting UNT Libraries Government Documents Department.