investigating the feasibility of a travelling-wave chopper for the clean separation of 10 mhz...

INVESTIGATING THE FEASIBILITY OF A TRAVELLING-WAVE CHOPPER FOR THE

CLEAN SEPARATION OF 10 MHZ BUNCHES - AT HIE-ISOLDE

Abhisek Mukhopadhyay

ABHISEK MUKHOPADHYAY 2

About me!• Budding Engineer –In my final year of

undergraduate study.

Major: Electronics and Communication Engineering

National Institute of Technology, Durgapur.

India


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 ?


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.


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


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.


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.

Discarded bunch 2

Discarded bunch 1 Beam axis(x)

Fiel

d ax

is(Z)

Strong Electric field region Weak fringe field region

Weak fringe field region

dl

hBunch separation

Deflected discarded bunch trajectory

One of the capacitors in the chopper


Time

Chopper field

Time

Intensity

Discarded Bunches

Nominal bunches

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• 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.


Falling field

Rising field

Sleeping field


N D

Field starts turning off

b1

-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,


N D

Field is completely off

b2

-b2

D

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.


ND

Field starts turning on

b3

-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.


N

Field is completely on

b4

𝑑 h𝑏𝑢𝑛𝑐

D

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.


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


Using g(x) to extract relevant fieldsThis is the point from which the discarded bunch in front sees the field falling


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%.


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


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.

Grounding plates

Beam axis

Top view

d

d2


d2


Parameter studies


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.


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


3ns Field

strength

5ns 3ns

Positions at which the nominal bunch sees the field turning off


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.


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

dx

Kick due to individual units


Introducing shielding plates

s sle=4mm

dUnit structure of the system

𝑙𝑠𝑡𝑟𝑢𝑐𝑡


Advantage:Reduces spatial extent furtherShielding capacitors can be biased to compensate kick to nominal bunches

Disadvantage:Reduces field intensity.More number of units.


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.

Main variable that changes the field profile

Fixed at 4mm


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).


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

2. We assumed that the pulsing wave travels uncorrupted. This might be difficult to achieve.

3. Perfect superposition of field elements.


Thank you!!

investigating the feasibility of a travelling-wave chopper for the clean separation of 10 mhz...

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