Tevatron Dipole measurements at MTF

The measurement setup

During September and October of 1996, two Tevatron dipoles were measured at MTF. The purpose of the testing was to measure the behavior of B2 under conditions germane to deceleration. The two magnets tested were TC0504 and TC1052. TC1052 was removed from the tunnel in 1985 for poor quench performance, even though the MTF data shows the saver cycle quench current to be 4236.4 amps. I have no information about the history of TC0504. The MTF data shows the saver cycle quench current to be 4233.4 amps.

The measurement apparatus used for this cold run was "new", so there was some time spent learning about making the measurements and interpreting the data. The probe used was an 18" long Morgan coil with both the dipole and the sextupole windings used. The probe was turned at 5 Hz, and data was collected at 32 points per rotation. For a small sample of the data, 64 points per rotation were collected in an attempt to get better 18 pole data for calibration of the probe radius. Four precision digital integrators were used for data collection. Two PDIs were used for sextupole probe coil, and two were used for the dipole probe coil. A PDI would collect data for just over 25 seconds, and then the other pair would collect data. The data from the first pair would download to disk while the second set collected data. In this way, continuous data collection could occur for arbitrarily long periods of time. During the beginning of the run, many 25 second blocks of data would be missing because of VME bus errors. By the end of the run, this was not a problem. Before each measurement, the magnet was quenched. Most measurements then included at least two identical cycles so that the cycle to cycle variation following a quench could be measured.

To deal with this problem, the ramp was modified. The rapid ramp rate was used from 400 to 642 amps. The overshoot occurred at this lower current and the current program stayed at 642 amps for 1 minute and the power supply was allowed to regulate. The current was then ramped up to the injection current of 662 amps at 1 amp per second. This deviation from the Tevatron waveform compromises the data less than the overshoot would.

Data cycles

TC0504 was put on the stand first, and commissioning of the measurement process began. A series of cycles were run to measure the B2 hysteresis at ramp rates of 10, 20, and 40 amps per second. These ramps had a constant di/dt for acceleration and deceleration. All other ramps were of the "shape" anticipated to be used in Collider Run II. All of the Collider cycle measurements on TC0504 had a 1 minute back porch and a 15 minute front porch. The cycle began with a ramp from zero current to the flattop current. Data collection began near the end of the flattop and continued through the back porch, the front porch, and the following ramp to flattop. A series of measurements were made at 4000 amp flattops with flattops lengths of 10 minutes, 30 minutes, and 60 minutes. Also, a series of measurements were made with flattops of 10 minutes, but with flattop currents of 4000 amps, 3552 amps, and 2664 amps. After these measurements, MTF switched to LHC related measurements for some time.

TC1052 was put on the stand after the LHC tests. The hysteresis measurements were repeated for this magnet, and then a series of flattop length measurements were done. The flattop lengths used for these measurements were 60, 10, 5, and 2 minutes. We then changed the back porch dwell time to 10 minutes and continued with more flattop length measurements. Data was collected with flattops of 60, 30, 10, 5, 2, 1, and 0.5 minutes. We then made series of measurements where we varied the number of cycles following a quench before we went into a store. At the end of the run, the temperature was dropped to 3.5 K and a measurement was made at 4440 amps. There were two measurement cycles made with the probe moved closer to the end of the magnet.

Measurement Data

Most of the data analyzed is sextupole data on the front and back porches. The data is most easily analyzed when plotting against ln(t+c) where c is some constant time that makes the data best fit a straight line. The value of c is different for various data cycles. The first data shown summarizes the effect of the flattop length on the cycles with a 10 minute back porch. Only TC1052 had data with the 10 minute back porch. All of this data was collected with a 4000 amp flattop. Below are plots of the normalized B2 measurements as a function of time on the front and back porches.

The fits to these log plots were made using the linear fit function in Kalidagraph. Values of c were chosen, by trial and error, such that Kalidagraph gave the "best" fit. The table below shows the parameter values obtained with this method.

It is clear that by choosing identical values of c, the two data sets are much more consistent. This arbitrary setting of parameter c does not significantly affect the quality of fit of the original data.

From the data above we will be able to parameterize the b2 drift on the back porch as follows:

b2 = b2i + (m* ln(t +c))

where t is the time since arrival on the back porch. Values for the coefficients in this equations are:

These coefficients will have to be determined with beam at the start of the collider run once we have chosen a temperature profile in the ring and an operating flattop energy.

By the time the first front porch begins, the magnet will have a history that depends on the back porch length, so each front porch data set will be shown with the value of c that best fits the data.

From the data above we will be able to parameterize the b2 drift on the front porch as follows:

b2 = b2i + (m* ln(t +c))

where t is the time since arrival on the front porch. Values for the coefficients in this equations are functions of both flattop length and back porch length. For a 10 min and 1 min back porch, we can state the coefficients as follows for TC1052:

It is possible that the coefficient c also needs to be a function of flattop length and or back porch length. More measurements would have to be made to parameterize the functional relationship between the back porch length and the coefficients above.

We made a series of magnetic measurements on cycles with different flattop energies. TC0504 was used for these measurements, and all cycles had a 1 minute back porch. The hysteresis curves for the different energies are shown below. Except for the top current for each cycle, the hysteresis curves are nearly identical for all three energies measured.

B2 Hysteresis loop at 600, 800, and 900 GEV

There is variation, however on the low energy porches when the flattop energy is varied.

The above plot shows the time dependent B2 on the front porch with different flattop energies. The following plots summarize the coefficients for the fits to b2=b + m*ln(t+c) for cycles of different energy flattops. The ramps all had a 1 minute back porch, 15 minute front porch, and a 10 minute flattop.

Back porch data above

front porch data below

The plots show that a flattop energy change of 100 GEV should cause an initial chromaticity difference of about 5 units on an injection level porch (with this particular ramp profile and porch lengths). Also, the speed of the b2 decay increases with increasing flattop energy. The next collider run should take place at a single energy that is determined before beam commissioning begins. Given that scenario, we should not have to modify our correction algorithms based on ramp energy.

During previous Collider runs, it was believed that if we ramped the Tevatron 6 times before initiating shot setup, the history of the Tevatron would be "consistent" from shot to shot. The number 6 was arrived at from beam studies. Ramping 6 times made the Tevatron "rather indifferent" to its previous history, while fewer ramps allowed previous history to have more impact on the beam conditions. During this run at MTF, we wanted to examine the choice of 6 ramps as a standard procedure.

For this measurement, the dipole was quenched on the stand and then cooled back down. Then the magnet was ramped to flattop with the normal HEP waveform (modified as explained above). At the end of the 30 second flattop, the magnet was ramped down, left at the back porch energy, cycled to 400 amps and back to a 1 minute pre-porch at 642 amps. The magnet was then slowly ramped to its injection energy at 1 amp per second. A one minute front porch preceded the next ramp to flattop. The measurement cycle started at the end of the first flattop following the quench. The number of ramps as described above following this was varied between 1 and 6. After the last ramp in each case, we stopped the ramp for a 15 minute front porch to look at the time dependent b2. The plot below shows that varying the number of ramps had almost no detectable effect on the b2 measurement on the front porch.

The ramp waveform we used was different than that used in the collider runs, but it is interesting to note that varying the number of ramps after a quench had almost no impact on the b2 drift on the front porch.

Near the end of this MTF run, some data was taken with a 1 TEV flattop at 3.5K. Also, data was collected with the probe moved to a z position neared the end of the magnet. I am not sure enough of the details of these data runs to comment on the data.

These final remarks are based on assumptions about how the Collider will operate during run II. The assumptions include the following statements:

The entire run will operate at one flattop energy to be determined before beam commissioning begins.

The magnet temperature profile around the ring will be similar for every store during the run.

We will not do any extra ramps between stores to establish a known history in the Tevatron.

The ramp rate will not change during the Collider run.

Using the above magnet measurements, we can make certain statements about how we will compensate for the b2 component in the dipoles. These statements concern only the preprogrammed compensation that we will introduce. I will say nothing here about using beam measurements to compensate for chromaticity changes other than it would be valuable to pursue those techniques as well.

The form of the compensation on the back porch will be

b2 = b2i + (m* ln(t +c))

b2i , and m depend on the time spent at flattop previous to the back porch. The value for c can probably stay fixed for all stores. At the beginning of the run, beam measurements will be made to determine the best functions for b2i , m, and c. We will load compensation tables to our chromaticity sextupoles every store before we decelerate.

The form of the compensation on the front porch will be the same. The difference is that the coefficients are a function of back porch length as well as the previous flattop length. Not enough magnetic measurements have been made to fully characterize these coefficients. Another set of magnet measurements may be in order. Beam measurements at the beginning of the run will definitely be needed to determine the best functions for the compensation coefficients. We will load compensation tables to our chromaticity sextupoles between extraction of the last antiproton, and injection of the first proton bunch.