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**Power Supply Regulation in the NuMI**

**Primary Proton Beamline**

**Peter Lucas, Nancy L. Grossman, June 24, 2001**

**[Primary Beamline Stability Constraints:]{.underline}**

The NuMI primary proton beamline contains seven bends. Of these four are
purely vertical and three are for strings of rolled magnets. Of the
three rolled strings only one, HV101, has its primary bend component in
the horizontal. Two different criteria have been developed to set
stability limits on the excitation currents for these bend strings. One
is that no current variation lead to an excursion from the design
trajectory along the line greater than 1mm RMS. The second is that no
single string lead to RMS motion at the target of greater than .25mm.
The first criterion comes from the need of having a stable beamline with
well-defined tuning characteristics, and the second is related to the
physics of the experiment. These criteria lead to the following
stability limits for the supplies powering these bend strings, where
instability in ppm is the plus or minus variation allowed in that loop
relative to its operating current at flattop.

Table 1: Power Supply Regulation Requirements: Filters

  -------- --------- --------- --------------- ------------- ------------- -----------
  String   Maximum   Peak      Corresponding   Allowed       Variation due Variation
           Current   Current   target RMS in   Instability   to 720 Hz in  due to 720
           of PS     (amps)    microns         in ppm        ppm with no   Hz in ppm
                                                             Filters       with
                                                                           Filters

  Lam60    2500      1445      240             200           298           21

  V100     5000      2786      200             400           660           25

  HV101    2500      1449      250             65            214           14

  V104     2500      1449      75              200           248           21

  V105     5000      4254      170             60            254           7

  V109     1250      880       250             200           216           23

  V110     2500      1210      250             55            207           17
  -------- --------- --------- --------------- ------------- ------------- -----------

A number of comments are in order concerning these values.

-   The time scale over which the variability occurs affects how large
    that variability is allowed to be. Any drifts which have a time
    scale of minutes or longer will be corrected in the tuning procedure
    by trims. Thus the variability on this time scale is allowed to be
    larger. If the variability time scale is related to power line
    ripple, the full effect will not be seen in that the extraction
    takes place over 10μs and will be at the same line phase for each
    cycle.

-   How the effects of the several strings combine with each other
    affects the level at which any string may vary. If the changes were
    truly random, then the RMS deviations at the target in particular
    would add in quadrature. This would lead to a targeting precision of
    565 microns, which exceeds the allowed error budget. If the
    corrections were to add linearly, there would be almost complete
    cancellation among the different vertical contributions, since
    different strings contribute in different directions. But, as is
    noted above, if the variations are slow enough they will not combine
    by either of these methods as each variation will be corrected by a
    trim.

# Power Supply Regulation

The present cost estimates for the NuMI beamline power supply regulation
includes costs for standard regulation plus the costs of a filter for
three of the seven magnet strings. The recent analysis of beam stability
and beam loss in the primary beamline specifies the power supply
regulation needed for the NuMI beamline. The tightest constraint is on
the V105 string and thus this is the string that the following
discussion centers around. The same levels of regulation (or less) can
be applied to the other strings. Here we revisit the issue of power
supply regulation in light of these recent results.

There are three sources of current variation for magnet strings. One is
the 720 Hz power supply voltage ripple being applied to the magnets. The
other two sources of current variation are line voltage changes and load
changes. Simulations of a particular power supply (or series of power
supplies) can be used to see the effects of these changes on the
resulting flattop current.

Filters are used to smooth out the 720Hz voltage ripple applied to the
magnets. When a PS voltage is changed, even if it is line-synched, it
shifts slightly on the 720Hz ripple, which is quite sharply peaked. As a
result, there is a fair amount of current variation despite line
synching. Even extraction can vary by up to 30 microseconds. Table 1
shows the current variation that would occur assuming no filters, for
each string. It is not acceptable as it is above the required stability
for beam on the target. With filters the current variation due to 720 Hz
line ripple is well below that needed for the NuMI beamline (see Table
1).

Line voltage changes were simulated for the NuMI V105 string (the MRPS).
Assuming a constant reference voltage, a 5% change in line voltage was
easily corrected for at the level of 100 ma (at a flattop current of
4250 amps) by the standard voltage regulation loop of the power supply.
This corresponds to \~24 ppm change. This level of line voltage change
is the most one would expect and results in a current variation well
below that required by NuMI.

Load changes were similarly simulated for the NuMI V105 string. A 5%
change in load resistance (corresponding to about a 10^O^ C change in
the copper of the magnet, or the LCW changing 15^0^ C) resulted in a 1
amp change out of 4250 amps. This corresponds to a 240 ppm change, which
is not acceptable by Table 1. Other magnet strings have not been
simulated, but would probably come to a similar result.

The conclusion is that filters are needed for every magnet string listed
in Table 1 (\~\$10K/string) and that some additional level of regulation
is needed to off set the changes that will occur due to load changes.
Autotune will greatly help, but has its drawbacks as one must have beam
and working beam position monitors to use Autotune. When beam first
starts up, Autotune will not be able to correct things immediately. Thus
we will use both Autotune and an additional level of power supply
regulation. In addition, each string will be tuned for the maximum
bandwidth. This is the standard way of starting up a power supply
system. The load change of \~240 ppm corresponded to a 20 Hz bandwidth,
as that is the level that can be obtained at worst. It is possible that
some or all of the NuMI strings could be tuned to a 40 Hz bandwidth and
this would halve the current instability (240 ppm goes to 120 ppm for
the V105 string). But this can not be guaranteed as instabilities can
occur. For the V015 string, this is still a factor of 2 away from the
desired value in Table 1. The thought is, though, that if the PS
regulation can get to within a factor of two of the desired level,
Autotune in combination with the PS regulation should provide the level
of regulation NuMI needs.

Three relatively standard items can be added to each string to increase
the current stability. The question is does NuMI need all three? The
first level of increase in regulation is the HOLEC transductor. The Main
Injector P1 power supply HVF12 is very similar to NuMI's V105 string. It
has a HOLEC transductor and studies are under way to see how well the
current is regulated with only the HOLEC transductor (\~\$5K/string). It
is estimated that a HOLEC transductor and the "standard" special
regulation electronics box (\~\$5K/string) will regulate to \~120 ppm
for the V105 string. As stated before, it is thought that then Autotune
would be able to keep the current stable to within +/-60 ppm. Also, if
the bandwidth can be increased to 40 Hz, then V105 would be at +/-60
ppm.

The third item that can be added is the BULB (\~\$5K/string). It is a
very complex device (like MECAR) that learns the complete ramps (and can
learn several ramps) and regulates throughout the process. It would
perhaps get the PS regulation down to a level of \~10 to 20 ppm. This is
thought to not be necessary for the NuMI beamline. Table 2 shows the
maximum resultant expected variation (+/- ppm) with the HOLEC
transductor and the special electronics. It also shows the extra factor
needed for each loop, assuming 20 Hz bandwidth and no help from
Auto-tune. It is believed that tuning for bandwidth and Auto-tune should
then make the current variations/beam movement, acceptable for NuMI.

Table 2: Power Supply Regulation Requirements: Load Changes

  -------- --------- --------- --------------- ------------- ----------------- ------------
  String   Maximum   Peak      Corresponding   Allowed       Instability in    Extra Factor
           Current   Current   target RMS in   Instability   ppm with Filters  Needed
           of PS     (amps)    microns         in ppm        & HOLEC & Special (reg/spec)
                                                             Electronics       

  Lam60    2500      1445      240             200           173               0.87

  V100     5000      2786      200             400           179               0.45

  HV101    2500      1449      250             65            173               2.65

  V104     2500      1449      75              200           173               0.86

  V105     5000      4254      170             60            118               1.96

  V109     1250      880       250             200           142               0.71

  V110     2500      1210      250             55            207               3.76
  -------- --------- --------- --------------- ------------- ----------------- ------------

Thus the regulation for the NuMI main magnet strings would consist of
filters (\~\$10K/string), HOLEC transductors (\~\$5K/string) and special
regulation electronics (\~\$5K/string). For those stings (four) where a
filter was initially not assumed to be needed, the cost is
\~\$20K/string. For the three strings where a filter was already
included in the cost, it is \$10K/string. Thus the estimated total cost
increase for power supply regulation of the primary beamline is \$110K
in FY 2001 dollars. Most of this cost could be delayed to FY2003. Since
the filters are items that are refurbished (a new one is \~\$35K), NuMI
needs to claim those by removing them from their present locations to
MI60 and MI62. This should be done ASAP.

The other costs can be delayed to perhaps the benefit of the NuMI
project. Study of the Main Injector P1 line regulation is under way to
determine the current stability resulting from the various levels of
regulation electronics used as a Fermilab exercise (at no cost to the
NuMI project). Also as a Fermilab exercise other options that are more
simple and thus less expensive than the special regulation electronics
or the BμLB system may be designed for Fermilab use as a whole. These
may result in a less expensive regulation system for NuMI than what is
stated above. Two of these possible options are described below.

A simplified version of the special regulation electronics may be
designed. The present system is relatively sophisticated, but it is
designed and has been built and tested. A simpler version would require
design time and testing, but the overall cost would be less. Another
option is to sample and correct the current part way through flattop.
With NuMI's flattop of 100 msec, this is possible. This would take some
time to design, build and test. But if this were done with non-NuMI
funds and was ready for implementation for NuMI at a reasonable cost,
NuMI could use it.

The remaining types of power supplies in the primary beam line are 20 KW
PEI's for the quadropole magnets and Main Injector (MI) trim power
supplies. The 20kw PEIs have standard regulation of +/-0.05% of the
maximum current of the power supply (100 or 200 amps). This corresponds
to an operating current variation of up to 0.44%. The MI trim magnets
standard power supply regulation is +/-0.1% of the maximum current of
the power supply (15 amps). We believe that this level of regulation is
sufficient for the NuMI beamline.