1/19/06 Klystron Linearizer PEP-II MAC Review January 19, 2006 D. Van Winkle, Claudio Rivetta, Dmitry Teytelman, John Fox, Themistoklis Mastorides, Jim Loudin, Mike Browne

1/19/06 Intro… This is a “linearizer” talk…. However, we have learned a few things along the way which I’d also like to illuminate here because they are relevant to the current discussion.

1/19/06 Outline Background (Why are we exploring linearization?) Other Options (Are there other options for impedance control?) Basic Idea (How will we do it?) Complexities (Why is it not simple?) Progress (What have we been doing?) Plan for Implementation (Rough Estimate) Conclusions

1/19/06 Background Info

1/19/06 Background (1) Measurements in the HER in 2003/2004 (Run 4) Showed significantly higher low mode longitudinal growth rates than our linear model predicted (up to 10X). These growth rates have been controllable at the present (and near future) currents. (With help from new low group delay woofer, and vigilant tuning of LLRF ). Plans through 2008 include much higher beam currents in both the LER and the HER. (4000mA LER on 2200mA HER) Our modeling shows that we will run out of low mode longitudinal control at some point before 2008 using the existing LLRF and low group delay woofer. Why do we need a linearizer?

1/19/06 Background (2) Ongoing modeling work done by Claudio Rivetta and Themis Mastorides shows correlation with measured data and allowed us to predict growth rates up to 4A in the LER. This is a work in progress and we need more measurement validation. A key contributor to these growth rates has been shown to be Klystron Saturation (as presented at previous MAC).

1/19/06 Simulation Results This output from the time domain non-linear simulation shows the effect of klystron saturation on growth rates Each point “tweaked” for 60 degree phase margin using “production algorithm” Even though it looks like we have damping up to 8 ms -1, these are extrapolated points. We know that at 3 amps we are running into loop phase margin limits above which we will not be able to use the “free” gain from the beam. Slide Change

1/19/06 Background (3) Why do we see this effect predominantly in the HER? –The HER is power limited at maximum beam currents (1800mA), so stations are required to run much further into saturation. The LER with 4 stations at 2.5-3A is not as power limited.

1/19/06 Background (4) Why does Klystron Saturation have an effect on growth rates? –Klystron Saturation reduces the effectiveness of the direct and comb loop impedance control due to the reduced small signal gain in saturation –We can not compensate via increased direct loop gain because the direct loop gain also affects the phase “gain” of the direct loop. This can lead to instability in the loop itself.

1/19/06 Background (5) Higher beam currents require higher drive set points to achieve the required output powers. As drive power is pushed up the small signal gain: (dPo/dPi) is reduced. Slide swap

1/19/06 Background (6) Another way to visualize this is to think of the feedback loops as gain and phase instead of I and Q. With amplitude and phase loops the problem is seemingly simple. –Simply Adjust the gain of the amplitude loop to compensate for the small signal gain loss due to klystron saturation. –The phase loop remains unaffected. Unfortunately in our (IQ) loops, both gain and phase are affected by direct loop changes.

1/19/06 Background(7) Suppose we have a vector representation of the 476 signal with some modulation around it (the circle). If this signal goes through a compressed klystron, the amplitude modulation will be compressed. Increasing the direct loop gain can restore some of the amplitude modulation swing, but also “distorts” the phase modulation. I Q The linearizer acts only on the amplitude, so the phase is not affected

1/19/06 Other Options

1/19/06 Other Options What options are we exploring? –Klystron Linearizer (the subject of this talk) –Simply increase direct loop gain (direct loop stability margins) –Complex gain adjustment in RFP (still investigating) –Asymmetric comb filters in comb II modules

1/19/06 Basic Idea

1/19/06 Basic Idea The basic idea is to measure the input and output Take the difference of the two and apply it as a correction to the input.

1/19/06 PEP II LLRF Where does this thing go in the LLRF?

1/19/06 Complexities

1/19/06 Complexities Loop Gain is given by K2*L*G(d)*Vi A function of Vi? A function of G(d) Since we hold d (the drive) constant on the klystron, and since the loop gain is a function of the gain of the klystron; As we increase beam current, both G and Vi increase resulting in the loop gain changing like vi^2

1/19/06 Complex Solutions To rectify this loop gain variation, we use a slow (injection rate) 1/X^2 compensator. This is done using a slow calculation in a small CPU board.

1/19/06 More Complexities Linearizer pre-distorts klystron input signal to get larger output swing However, if we go “over the top”, the feedback sign flips!

1/19/06 Small Signal Gain Small signal gain compression changes are also a function of drive set point. 10 W 20 W

1/19/06 Implications Need to measure small signal gain of Klystron as we increase output power (increase beam current) to keep bandwidth constant. –This will be used to generate a further correction factor independent of klystron characteristics. The bottom line is that a simple 1/X^2 compensation will not be enough.

1/19/06 Progress

1/19/06 Where are we? Progress to Date –Built 4 prototype linearizers and installed in LER to test effectiveness –Tested 3 linearizers on Beam –Tested one prototype with live Klystron in test stand –On cusp of finishing design for full blown EPICs based configurable klystron linearizer

1/19/06 Beam MD results 4 of these built and installed in LER

1/19/06 Beam MD results Tested with beam –Had a mistuned Parked cavity and different drive level (saturation level): –After proper tuning….very little difference No Linearizer Higher Saturation Linearized

1/19/06 Beam MD conclusions Mistuning of parked cavity forced us to retake our data. Due to excess noise in the LLRF we had to turn down the drive set point on the klystrons (during linearizer MD…this was to avoid “going over the top”). –Since we had already done the baseline grow-damps with higher drive set points, we had to go back in and do some quick re-measurements The result from the grow-damp MD are inconclusive because the klystrons were operating well out of saturation. To definitively show linearizer effectiveness, we must compare heavily saturated klystrons against linearized klystrons. To show this effect in the LER requires station operating points well into saturation. Unfortunately we were not able to operate at these saturations levels due to excess noise from the LLRF system. We now know how to configure all stations to show this effect and are ready for another MD.

1/19/06 Noise reduction In the beam MD noise in the LLRF system prevented operating the klystron in heavy saturation. Subsequently we did a short MD (no beam) to see if re-partitioning the gain in the RFP module could help reduce the noise coming from the gap reference. We had success in reducing the noise (special thanks to Mike Browne)– Ready for another MD with beam.

1/19/06 Test Stand Measurements Test stand measurements are very important for testing basic linearizer operations The test stand measurements educated us on the variability of Klystron gain curves

1/19/06 Test Stand Results Each Klystron has a unique operating characteristic. Small signal gain at each HVPS set point varies significantly This further complicates the bandwidth variation of the linearizer. And…explains why we set up the direct loop at maximum output power.

1/19/06 Test Stand Results For example, our bench measurements with a klystron “model” show good bandwidth control.

1/19/06 Test Stand Results Necessity for additional dynamic linearizer compensation With static 1/x^2 compensation we see large variations in closed loop bandwidth. Measurements with a klystron in the test stand show another reality…

1/19/06 Next Steps MD2 with beam (higher klystron Saturation). –Modeling used to specify LER operating point to show saturated effects (similar to HER). –Careful measurements of growth rates with and without linearizer. Klystrons will be in heavily saturated state. This MD will be the decision point for before final production linearizer development.

1/19/06 More Detailed Plan

1/19/06 Next Design Steps Need to implement: –Limiter on output of linearizer (“to prevent going over the top”) –Imbedded loop gain measurement –IOC control –Complex imbedded algorithms –EPICs interface

1/19/06 Block Diagram Complexities now include: Circuitry to compensate for differing klystron characteristics with HVPS changes Circuitry/algorithms to compensate for drive set point Electrically controlled attenuators for operating point adjustment IOC interface

1/19/06 Resources Software Engineer (5-6 person months) Hardware Engineer (6 person months) EPICs interface person (3 person months) Technician (6 person months) If the decision is made soon, we should be able to finish the linearizers for run 6 (pending availability of resources)

1/19/06 Conclusions This development will add another layer of complexity to a already complex LLRF hardware and software system. This is not trivial! We think linearizers will be necessary to reach the planed beam currents We have not yet definitively shown the linearizer effectiveness (a further MD is required) There may be other techniques which may help to reduce the growth rates: –Asymmetric comb filters –Asymmetric RFP gain adjustment –We are using the time domain simulation to study these options We are moving ahead on the assumption that we will be building and installing klystron linearizers