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 National Institute of Technology, Durgapur. India ABHISEK MUKHOPADHYAY 2

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 ? ABHISEK MUKHOPADHYAY 3

About the beam! ABHISEK MUKHOPADHYAY 4

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. ABHISEK MUKHOPADHYAY 5 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

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. ABHISEK MUKHOPADHYAY 6

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. ABHISEK MUKHOPADHYAY 7

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

Time Chopper field Time Intensity Discarded Bunches Nominal bunches ABHISEK MUKHOPADHYAY 9 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. we would like to kick 9 out of every 10 bunches. We are also worried about the field seen by the nominal bunch, when the adjacent one is being kicked and the chopper is on.

Simulating the on/off characteristics ABHISEK MUKHOPADHYAY 10

Falling field Rising field Sleeping field ABHISEK MUKHOPADHYAY 11

ABHISEK MUKHOPADHYAY 12 N N D Field starts turning off 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,

ABHISEK MUKHOPADHYAY 13 N N D Field is completely off b2 D And define b2 as that point after which the nominal bunch sees a completely off field.

ABHISEK MUKHOPADHYAY 14 N N D Field starts turning on b3 And define b3 as that point after which the nominal bunch sees the field turning back on.

ABHISEK MUKHOPADHYAY 15 N N Field is completely on b4 D And define b4 as that point beyond which the nominal bunch sees the field back on.

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, ABHISEK MUKHOPADHYAY 16

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

Performance parameters We have two key results of concern. 1. The integrated kick faced by the bunches. We define them for the three case of bunches as: 2. The ratio of kicks faced by the nominal bunch to the kick faced by the discarded bunch. It must be kept below 1%. ABHISEK MUKHOPADHYAY 18

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. ABHISEK MUKHOPADHYAY 19

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. ABHISEK MUKHOPADHYAY 20

Grounding plates Beam axis Top view d d2d2

d2 ABHISEK MUKHOPADHYAY 22

Parameter studies ABHISEK MUKHOPADHYAY 23

The ratio does not change much when we increase the length. It is just about the tolerable limit when l is below 12mm. 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. ABHISEK MUKHOPADHYAY 24

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3ns3ns Field strength 5ns 3ns Positions at which the nominal bunch sees the field turning off ABHISEK MUKHOPADHYAY 26

Part II- Practical constraints For practical purposes we have the following constraints to overcome, 1. The length of the complete structure should be below 500mm. 2. The ratio of the kicks should be below 1% 3. The cumulative kick faced by the discarded bunches should be around 11kV. ABHISEK MUKHOPADHYAY 27

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 ABHISEK MUKHOPADHYAY 28 dx Kick due to individual units

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

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

ABHISEK MUKHOPADHYAY 31 Main variable that changes the field profile Fixed at 4mm

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

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). ABHISEK MUKHOPADHYAY 33

Structure seems practically feasible! Yet… We did not consider: 1. Finite length of the bunches and focussed our calculations on the bunch centre. Would work on it next week 1. We assumed that the pulsing wave travels uncorrupted. This might be difficult to achieve. 2. Perfect superposition of field elements. ABHISEK MUKHOPADHYAY 34

Thank you!! ABHISEK MUKHOPADHYAY 35