10.91 RFMODE—A simulation of a beam-driven TM monopole mode of an RF cavity.

A simulation of a beam-driven TM monopole mode of an RF cavity.
Parallel capable? : yes
GPU capable? : no
Back-tracking capable? : no

A simulation of a beam-driven TM monopole mode of an RF cavity.

A simulation of a beam-driven TM monopole mode of an RF cavity.

A simulation of a beam-driven TM monopole mode of an RF cavity.

A simulation of a beam-driven TM monopole mode of an RF cavity.

This element simulates a beam-driven monopole mode cavity using the fundamental theorem of beam loading and phasor rotation. In addition, a generator-driven field may be included using a feedback system [44].

Note on phase conventions: the phase convention for the PHASE_SETPOINT parameter of RFMODE is the same as for the PHASE parameter of RFCA. However, in the output files from RFMODE, i.e., the files requested with the RECORD and FEEDBACK_RECORD parameters, a different convention is used, which differs by -90 degrees from the PHASE_SETPOINT parameter.

The feedback implementation uses either amplitude and phase feedback or else in-phase and quadrature feedback. Figure 3 shows the model used for the feedback system. More information is available in [44].

Rf feedback is active when a non-zero value is given for DRIVE_FREQUENCY and when either AMPLITUDE_FILTER and PHASE_FILTER or else IN_PHASE_FILTER and QUADRATURE_FILTER are given. These parameters name SDDS files that define filters in the z domain

(140)

which translates into the discrete time domain as

(141)

where y[n] is the filter output (e.g., additional generator current) and x[n] is the filter input (e.g., the voltage error signal). The filter files must each contain two columns:

• denominator — The a_i filter coefficients. These should generally sum to zero or nearly zero.
• numerator — The b_i filter coefficients. These are generally very small.

Each file can consist of up to four pages, with each page representing one filter in a parallel filter bank formed from all pages. The output of the four stages is added to obtain the control signal. The number of rows in the page is given by the larger of r or m; in the case of multiple pages, the number of rows in each page is given by the largest r or m from the highest order filter amongst the pages, by simply stuffing the rows of the other pages with zeros, i.e., rows representing orders of z down to z^-l where l is the largest r or m of the filter pages.

For example, a digital low-pass filter with DC gain of k can be specified as

(142)

where p is the frequency of the pole and T is the sample interval.

The feedback loop reads the cavity state and acts on the generator at a fixed interval (in buckets) of UPDATE_INTERVAL. The timing of this activity is aligned to the arrival time of the first bunch in the RFMODE element. By default (READ_OFFSET=0), the timing is such that the state is read just before the next arrival of that bunch; in particular, it is 180 degrees ahead of that arrival. If bunches are equally spaced by, say N_b buckets, the UPDATE_INTERVAL parameter should ideally be mN_b, where m > 0 is an integer. This ensures that the state is read at a fixed timing relative to the bunches.

The rf feedback feature makes use of the voltage amplitude measured when there is no bunch present. The RECORD file shows the voltage seen by the beam, computed by averaging over the voltage for each particle. These may deviate by values from a few percent to of order ten percent, depending on the loss factor for the cavity and the number of bunchess; this is caused by the fact that the rate at which an intense bunch removes energy from the cavity will typically, albeit briefly, exceed the power from the generator. To reduce the impact of this effect, one may use the ADJUSTMENT_FRACTION, ADJUSTMENT_START, and ADJUSTMENT_INTERVAL parameters to modify the voltage setpoint. If ADJUSTMENT_FRACTION is non-zero, then for every ADJUSTMENT_INTERVAL^th pass after the ADJUSTMENT_START^th pass, the voltage setpoint will be adjusted based on a comparison of the bunch-averaged voltage to the user’s setpoint. E.g., if the bunch-averaged voltage is 100 V too low and ADJUSTMENT_FRACTION is 0.1, the voltage setpoint will be raised by 10 V. Users should note that if ADJUSTMENT_FRACTION is too large or ADJUSTMENT_INTERVAL is too small, the system may be unstable.

Normally, the field dumped in the cavity by one particle affects trailing particles in the same turn. However, if one is also using a WAKE or ZLONGIT element to simulate the short-range wake of the cavity, this would be double-counting. In that case, one can use LONG_RANGE_ONLY=1 to suppress the same-turn effects of the RFMODE element.

Two output files are available: the RECORD file includes bunch-by-bunch data on the beam-induced fields and the total cavity fields. The FEEDBACK_RECORD file includes tick-by-tick data from the feedback system simulation; writing this file this can significantly degrade performance.

NB: when BUNCHED_BEAM_MODE is set to a value other than 1, in order to obtain the effect of several bunches while tracking only one bunch, the total charge set with the TOTAL parameter of the CHARGE element should equal the charge in a single bunch, not the entire beam. However, when BUNCHED_BEAM_MODE=1 (allowing an indeterminant number of bunches to be actually present), then TOTAL should be the total for all bunches together.

Explanation of <filename>=<x>+<y> format: Several elements in elegant make use of data from external files to provide input waveforms. The external files are SDDS files, which may have many columns. In order to provide a convenient way to specify both the filename and the columns to use, we frequently employ <filename>=<x>+<y> format for the parameter value. For example, if the parameter value is waveform.sdds=t+A, then it means that columns t and A will be taken from file waveform.sdds. The first column is always the independent variable (e.g., time, position, or frequency), while the second column is the dependent quantity.