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Abhisek Mukhopadhyay

Investigating the feasibility of a travelling-wave chopper for the clean separation of 10 MHz bunches - at HIE-ISOLDE. Abhisek Mukhopadhyay. About me!. Budding Engineer –In my final year of undergraduate study . Major: Electronics and Communication Engineering

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Abhisek Mukhopadhyay

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  1. Investigating the feasibility of a travelling-wave chopper for the clean separation of 10 MHz bunches - at HIE-ISOLDE Abhisek Mukhopadhyay

  2. ABHISEK MUKHOPADHYAY About me! • Budding Engineer –In my final year of undergraduate study. Major: Electronics and Communication Engineering National Institute of Technology, Durgapur. India

  3. ABHISEK MUKHOPADHYAY Part I • Beam specifications. • Set of parallel plate capacitors as a beam chopper? • Mathematics concerning the definition of kick factor and other performance parameters. • Defining real time weighting function f(t) for extracting relevant field elements. • Need for modifications ?

  4. ABHISEK MUKHOPADHYAY About the beam! • The average beam kinetic energy is 300 KeV/u This gives us an average beam velocity of ; • Post-accelerated radioactive beams at ISOLDE are currently delivered with a bunch spacing of 9.87 ns (75mm), defined by the RFQ frequency of 101.28 MHz • We need a minimum chopper aperture of 30mm for not losing acceptance.

  5. ABHISEK MUKHOPADHYAY A capacitor • A capacitor is a device that stores electric potential energy and electric charge. We would be using the parallel plate capacitor which consists of two parallel plates separated by Vacuum (in our case). We charge them with a voltage of 1KV. The separation and the plate structure are the parameters we can vary in order to manipulate the field produced. A real capacitor has fringe fields that increase the spatial extent of the fields outside of the plates. We used the CST-EM studio to simulate the actual field profile due to our customized structures

  6. ABHISEK MUKHOPADHYAY Kicker (chopper) • A kicker (chopper) is used to deflect the unwanted part of the beam, off the axis. • It can be conceptualized as a device that causes a transverse deflection selectively to a part of the beam. • So, a chain of capacitors that can turn on/off very quickly can be used as a chopper. Each of the capacitors in the chain are assumed to have their independent timing circuits and powering systems, and they do not couple with each other.

  7. ABHISEK MUKHOPADHYAY Our Assumptions • We think the bunches to be point charges at the bunch centre. • The travelling wave passes through the system uncorrupted. • Perfect electrical conductivity for the plates. • The bunches remain on axis, and significant deflection takes place only after a long distance.

  8. One of the capacitors in the chopper Discarded bunch 2 Strong Electric field region Weak fringe field region Weak fringe field region h Discarded bunch 1 Bunch separation Beam axis(x) Field axis(Z) Deflected discarded bunch trajectory d l

  9. ABHISEK MUKHOPADHYAY The main idea is to make a section of the beam face a strong field such that it deflects off axis, and negligible field for the remaining part such that it remains on axis. So the fields need to turn off and back on at precise time points. Nominal bunches Chopper field Time we would like to kick 9 out of every 10 bunches. Discarded Bunches Intensity Time We are also worried about the field seen by the nominal bunch, when the adjacent one is being kicked and the chopper is on.

  10. ABHISEK MUKHOPADHYAY Simulating the on/off characteristics • We consider a time varying pulse (f(t)) that is travelling with every nominal bunch and is symmetrically defined about the time at which the nominal bunch moves through the centre of the capacitor plates. f(t) can be mapped to a function of distance x along the beam axis, say g(x) using the transformation The main job of the pulse is to turn a capacitor unit off when a nominal bunch is passing through it and turn it back on when it has crossed it.

  11. ABHISEK MUKHOPADHYAY Falling field Rising field Sleeping field

  12. ABHISEK MUKHOPADHYAY Field starts turning off -b1 N D b1 We define b1 as that point on the beam axis at which if the centre of the nominal bunch reaches, the field due to the capacitor starts to turn off. To place the pulse symmetrically over the centre of the plates, we assign b1 with,

  13. ABHISEK MUKHOPADHYAY Field is completely off -b2 N D D b2 b2 We can map o a distance over which the field falls, And define b2 as that point after which the nominal bunch sees a completely off field.

  14. ABHISEK MUKHOPADHYAY Field starts turning on b3 N D -b3 We can map the sleep time T o a distance over which the field stays off, And define b3 as that point after which the nominal bunch sees the field turning back on.

  15. ABHISEK MUKHOPADHYAY Field is completely on N D b4 b4 We can map o a distance over which the field rises back to its initial strength as, And define b4 as that point beyond which the nominal bunch sees the field back on.

  16. ABHISEK MUKHOPADHYAY g(x) • From the practical borders of operation for the chopper, we can use b1,b2,b3 and b4 to create a piece-wise linear weighing function g(x) as, g(x) can be multiplied to corresponding field elements for the extraction of the actual field profile faced by the bunches

  17. ABHISEK MUKHOPADHYAY Using g(x) to extract relevant fields This is the point from which the discarded bunch in front sees the field falling

  18. ABHISEK MUKHOPADHYAY Performance parameters • We have two key results of concern. • The integrated kick faced by the bunches. We define them for the three case of bunches as: • The ratio of kicks faced by the nominal bunch to the kick faced by the discarded bunch. It must be kept below 1%.

  19. ABHISEK MUKHOPADHYAY Performance of a simple capacitor as a chopper unit In the beginning, We consider a set of standalone capacitors to make up the chopper. It gives impractical values of the ratio as defined earlier.

  20. ABHISEK MUKHOPADHYAY Modifications! The field profile due to a capacitor is too wide for being practically useful as a chopper unit. We could shrink the field extent by introducing an infinite grounding plane behind the plates. Other factors remaining same.

  21. Top view d2 d Beam axis Grounding plates

  22. ABHISEK MUKHOPADHYAY d2

  23. ABHISEK MUKHOPADHYAY Parameter studies

  24. ABHISEK MUKHOPADHYAY The kicks nearly double for a factor 3 increase in the length. The effect is more on the nominal bunch as the ratio is seen to increase with length. The ratio does not change much when we increase the length. It is just about the tolerable limit when l is below 12mm.

  25. ABHISEK MUKHOPADHYAY The increase in the kick faced by the nominal bunches is more compared to the increase in kick faced by the discarded bunches, as we decrease . The ratio deteriorates as we decrease

  26. ABHISEK MUKHOPADHYAY 5ns 3ns 3ns Field strength Positions at which the nominal bunch sees the field turning off

  27. ABHISEK MUKHOPADHYAY Part II- Practical constraints • For practical purposes we have the following constraints to overcome, • The length of the complete structure should be below 500mm. • The ratio of the kicks should be below 1% • The cumulative kick faced by the discarded bunches should be around 11kV.

  28. ABHISEK MUKHOPADHYAY Motivation • If, the capacitors are efficiently shielded from each other ( by efficient shielding we mean that one capacitor should not see a significant part of the field due to the surrounding units), the principle of superposition holds for the independent field elements (and their timing functions are independent.) We can claim that the total kick faced by a discarded bunch is the kick provided by an individual unit scaled up by the number of such units(N). So we can indeed predict a total structure just by studying one of its units dx Kick due to individual units dx

  29. ABHISEK MUKHOPADHYAY Introducing shielding plates le=4mm s s d Unit structure of the system

  30. ABHISEK MUKHOPADHYAY Disadvantage: Reduces field intensity. More number of units. Advantage: Reduces spatial extent further Shielding capacitors can be biased to compensate kick to nominal bunches

  31. ABHISEK MUKHOPADHYAY Optimizing • needs to be large enough that the influence of the previous unit on the next decreases. • Making large increases the length of the complete structure. • So we need to vary other parameters to maximize and minimize . • We studied the effect of various parameters on the vs relationship. Fixed at 4mm Main variable that changes the field profile

  32. ABHISEK MUKHOPADHYAY Increasing the length of the chargeable plates actually decrease the length.

  33. ABHISEK MUKHOPADHYAY Conclusion Assuming electrostatic limit is valid, • We can transmit the nominal bunch with less than 1% kick • Discarded bunches are kicked by 4 mrad (k=11kV). • With 1 kV excitation voltage on each plate the structure is less than 0.5m (we need 22 capacitors ,l=12mm).

  34. ABHISEK MUKHOPADHYAY Structure seems practically feasible! Yet… We did not consider: • Finite length of the bunches and focussed our calculations on the bunch centre. Would work on it next week • We assumed that the pulsing wave travels uncorrupted. This might be difficult to achieve. • Perfect superposition of field elements.

  35. ABHISEK MUKHOPADHYAY Thank you!!

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