Low Level RF Modeling for the MEBT Rebunchers

The four MEBT rebuncher cavities need control electronics to set their amplitude and phase to the values needed for proper beam propagation. The raw power to drive them (20kW to 40kW at 402.5 MHz) comes from commercially packaged grounded-grid triode amplifiers. The ``Low Level RF'' subsystem discussed in this note needs to:

• send an RF waveform to the triode assembly
• measure the cavity detune angle (tuner error signal)
• use EPICS for command and readback.

An architecture for this subsystem was reviewed on May 10, 2001. A digital signal processing section (based on an FPGA) is connected to a low latency measurement of the cavity field vector, and controls the RF drive vector sent to the triode amplifier.

At its simplest, the digital control unit could turn the RF output on for 1 ms after a 60 Hz trigger, and provide a readback of the cavity voltage waveform to the operator. Previous experience with the RFQ shows that the decay segment of this waveform can be analyzed to determine the cavity detune angle. The benefit of having a low-latency measurement/control loop is that digital feedback can be included with no additional hardware.

The body of this paper explains a numerical model of the RF system, and shows the expected behavior of the system. It shows how feedback and feedforward can be used to keep the beam loading transient under control.

I also provide documentation for how to work with the numerical model, which is provided in the form of a c program. The program, along with this tech note, are available for download.

You may download this Tech note in its entirety in PostScript (321K) or PDF (98K). The PostScript version can be printed on any PostScript printer, or previewed with the Ghostscript suite. The PDF version can be viewed and printed using any of xpdf, the Ghostscript suite, or Adobe Acrobat (untested).

The c program referenced in the article can be downloaded here. It should compile and run on any machine with a working c compiler, and a libc that implements getenv and printf.

You may download a kit (24K) that allows a complete regeneration of the note, including all simulation runs. This kit is tested on a Linux box with octave and LaTeX installed. Unpack it, and type "make" to get as far as the .dvi and .eps files. Other choices include "make print" and "make web".

You may look at the individual pieces, where all the figures are given in .eps form:

• LaTeX source file
• Figure 1. Block diagram of the system as modeled.
• Figure 2. Schematic of feedforward waveform structure.
• Figure 3. Triode saturation characteristics.
• Figure 4. Triode amplifier risetime.
• Figure 5. RX Filter amplitude and delay characteristics.
  • part a, close-in S21
  • part b, wide-band S21
  • part c, delay
• Figure 6. Cross-check of ODE code with analytic solution.
• Figure 7. Beam pulse transient as modeled by default parameters.
• Figure 8. Beam pulse transient for cavity 1.

ERRATA

• The figure 5 ordinate captions should be S21, not S11.
• In the ODE analytic test case, the time domain expression is written using a mix of t and x. They should of course both be the same, conventionally t.