Felix Marti Michigan State Universityostroumo/MSU/Lectures... · 2018. 10. 11. · Felix Marti....

This material is based upon work supported by the U.S. Department of Energy Office of Science under Cooperative Agreement DE-SC0000661, the State of Michigan and Michigan State University. Michigan State University designs and establishes FRIB as a DOE Office of Science National User Facility in support of the mission of the Office of Nuclear Physics.

Felix Marti

Michigan State University

PHY862 Accelerator SystemsCyclotrons

Content

Brief history of cyclotron development– Classic cyclotron– Thomas cyclotron– Sector focused (AVF) cyclotron– Separated sector cyclotrons– Separated orbit cyclotron

Basic cyclotron components – Ion source/ Axial and Radial Injection/Strippers– Magnet requirements– Extraction system

– RF system– Vacuum system– Beam diagnostics

Felix Marti PHY862 "Aceclerator Systems"

2Fall 2018

Main Stages in the Evolution of the Cyclotron

Classical cyclotron, flat pole magnet 1930.- Lawrence builds the first cyclotron Energy limitations.-

– Bethe and Rose (1937) Sector focused cyclotron.-

– Thomas (1938), experimentally Berkeley (1950) Spiral sectors.-

– Harwell (1955), Oak Ridge (1955), Berkeley (1957) H- acceleration.-

– Rickey & Smythe (1962) Separated sector cyclotrons (1970s) Compact superconducting cyclotrons

– 1981 MSU and Chalk River Very large superconducting cyclotrons

– K=2500 RIKEN (2007)

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Basic Relations

𝜔𝜔 = 𝑞𝑞𝑞𝑞𝑚𝑚

𝑝𝑝 = 𝑞𝑞𝑞𝑞𝑞𝑞

Rigidity = 𝑝𝑝𝑞𝑞

= 𝑞𝑞𝑞𝑞 = 𝑚𝑚𝑜𝑜𝛾𝛾𝛾𝛾𝑞𝑞

= 𝛽𝛽𝛽𝛽 𝑚𝑚𝑜𝑜𝑐𝑐𝑞𝑞

Radio Frequency 𝜔𝜔𝑅𝑅𝑅𝑅 = ℎ 𝜔𝜔𝑜𝑜– ωo = orbital frequency h = harmonic number

𝑞𝑞 = 𝛽𝛽 𝑚𝑚𝑜𝑜𝛾𝛾𝑐𝑐𝑞𝑞𝑞𝑞

= 𝛽𝛽𝑐𝑐𝜔𝜔𝑜𝑜

= 𝑅𝑅∞𝛽𝛽 𝑐𝑐 = 𝜔𝜔𝑜𝑜𝑅𝑅∞– 𝑅𝑅∞ = radius at which ion reaches speed of light at that orbital frequency

Cyclotron K value (non relativistic)

– T ( kinetic energy) = 𝑝𝑝2

2𝑚𝑚= 𝑞𝑞

2𝑞𝑞2𝑅𝑅2

2𝑚𝑚𝑜𝑜= 𝑒𝑒

2𝑞𝑞2𝑅𝑅2

2𝑚𝑚𝑢𝑢

𝑄𝑄2

𝐴𝐴

– 𝑇𝑇𝐴𝐴

= 𝑒𝑒2𝑞𝑞2𝑅𝑅2

2𝑚𝑚𝑢𝑢

𝑄𝑄𝐴𝐴

2= 𝐾𝐾 𝑄𝑄

𝐴𝐴

2𝐾𝐾 = 𝑒𝑒

2𝑞𝑞2𝑅𝑅2

2𝑚𝑚𝑢𝑢

– Bending power, may not reach that energy because of focusing limitations, there are other limitations like

– 𝑇𝑇𝐴𝐴

= 𝐾𝐾𝑓𝑓𝑄𝑄𝐴𝐴

𝐾𝐾𝑓𝑓 = focusing K

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Energy Gain

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( )tSinVV RFo ω=

( ) ( )

( ) ( )( )

( )( ) ( )( )

( ) ( )( )

( ) ( )

( )

=∆

=−=−

−=

−+=

+−=∆+∆=∆

=∆−=∆

2 2

width Dee spatial theis D where

but

2/2

2/.2/.2*

,

0

2121

210

12210

21021

202101

hDSinCosqVE

hDtthtt

ttSintCosqV

ttSinttCosqV

tSintSinqVEEE

tSinqVEtSinqVE

oRF

RFcenterRF

RFRF

RFRF

RFRF

φ

ωω

ωω

ωω

ωω

ωω

Gap 1

Gap 2

t1

t2

centerRF tωφ = is phase beam The

t2t1

Vdee

RF time

RF Harmonics: Example: 2 90o Dees

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First harmonic, h=1

Dees are 180 degrees out of phase

=

2hDSinaccη

Figure from Heikkinen, CERN Accelerator School: 5th General accelerator physics course, CERN 94-01, 1994

Second harmonic, h=2, dees are in phase

Third harmonic, h=3, out of phase

180o

270o

90o

The acceleration efficiency depends on the harmonic (h) and dee width (D)

707.0)135( 90,D 3,h000.1)90( 90,D 2,h707.0)45( 90,D 1,h

============

SinSinSin

ηηη

Smooth Acceleration Approximation

Assuming a continuous energy gain, we obtain for one turn:

𝑑𝑑𝑑𝑑𝑑𝑑𝑑𝑑

= 𝑞𝑞𝑉𝑉𝑜𝑜𝑛𝑛𝑔𝑔η𝑎𝑎𝑐𝑐𝑐𝑐 cos 𝜑𝜑 = 𝑞𝑞𝑉𝑉𝑚𝑚𝑎𝑎𝑚𝑚 cos 𝜑𝜑

The change in phase with energy is given by:

sin 𝜑𝜑 − sin 𝜑𝜑𝑜𝑜 =2𝜋𝜋ℎ𝑞𝑞𝑉𝑉𝑚𝑚𝑎𝑎𝑚𝑚

�0

𝑑𝑑 𝜔𝜔𝑜𝑜 − 𝜔𝜔 𝐸𝐸𝜔𝜔 𝐸𝐸

𝑑𝑑𝐸𝐸

Homework #1 : derive the change in phase formula shown above

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From this equation we see that for a given error in the magnetic field, ω≠ωo the phase change is proportional to the harmonic number and inversely proportional to the maximum energy gain per turn.

From this point of view lower harmonics are more favorable, and higher voltage is desirable.

Three Main Regions in a Cyclotron

Central region - Electric fields are very important, the electric fields are represented by detailed potential maps. We must:

• Clear the central region• Center the orbits radially• Provide enough vertical focusing

Acceleration region - The energy gain at the dee gaps can be approximated by delta functions. Two things that we have to be careful:• Maintain isochronism• Avoid dangerous resonances

Extraction region - Critical area!!! The edge field changes very fast. • The ions are not isochronous in the edge. High electric fields are needed in the

deflectors (except in extraction systems that use stripping). • Strong defocusing forces during the extraction path.

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Central Region: K500 Example with Spiral Inflector (1) RF electrodes (dees) located in the

valleys (2) Hills, closest gaps in the magnets (3) Central region

The central region is simulated utilizing software that calculates the electric field in 3D, utilizing a quasi static approach (distances are short with respect to wavelength). We assume that the electric field is given by the solution of the potential problem in the electrostatic case, multiplied by a factor that gives the time dependence as Sin(ωRFt). we can not extend the solution to the whole dee, because its size starts to become comparable with the wavelength in free space.The voltage along the dee gap will change, and this variation is more noticeable for the higher frequencies. In the MSU K1200 cyclotron at 28 MHz the dee voltage variation is of the order of 20%, with the highest voltage near extraction. It is good to have high voltage at extraction, increases the turn separation.

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1

1

12

2

2

3

Historical Note: Electrolytic Tank Analogue

Several electrodes at different potentials are introduced in an electrolytic tank and a probe is used to scan and measure the potential on the liquid surface. It is not an easy measurement, it can take many hours and the evaporation of the liquid must be compensated. Metal parts with the shape of the cyclotron electrodes must be machined.

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Vertical Focusing in the Central Region

One of the problems in the central region is to obtain enough vertical focusing to prevent the beam from blowing up and hitting the vertical gap

As the magnetic field harmonics of order N increase with radius as 𝑞𝑞𝑑𝑑 we cannot expect much contribution from the flutter to 𝑣𝑣𝑧𝑧 at small 𝑞𝑞 values.

It is common to put a “cone” in the magnetic field (𝑑𝑑𝑞𝑞𝑑𝑑𝑑𝑑

< 0) that contributes to a positive 𝑣𝑣𝑧𝑧2 but is usually insufficient. Now enters the electric field

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E field

median plane

Focusing | Defocusing

Ion trajectory

M. E. Rose,Phys. Rev. 53 (1938) 392.

Electric Focusing: Changing Strength The primary electric focusing effect in cyclotrons is the “phase effect”. If the ions cross the

gap when the field strength is falling, then the focusing impulse will exceed the defocusing impulse and a net focusing will result.

On the other hand if the field strength is rising then a net defocusing will result.

A higher order effect is the “acceleration effect”. The energy of the particle in the second half is larger than in the first half, and consequently it deflects less for the same electric force.

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Details on the Electric Vertical Focusing

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( )

2Z

22 2 2 2Z

It can be shown that the change in due to the electric focusing is given by:

sin cot cos sin4 4 2

Where is the RF harmonic, the phase of the beam

eh h hD D D

n n

h

υ

υ θπ π

∆ = Φ + Φ − Φ −

Φ

d turnd

with respect to the RF, D is the angular width of the dee,2and = , and N is the number of dees. The number of turns with T = kinetic energy, and T the energyN

gain per turn. This expre

eturn

TnT

πθ =

ssion neglects the "acceleration effect".

The first term is a focusing term for >0 (positive phases means that the beam is lagging the RF).

The second term corresponds to the alternating gradient fo

Φ1cusing. But this is a second order effect in . We see that both terms

decrease fast with increasing energy. The electric focusing is usually relevant only in the first few turns in the central region

n

2Z. After that we better have developed a flutter big enough to make positive !!!

It is common practice to move the source "back" in azimuth to delay the ions from getting to the gaps on time, makingυ

the phase more postive. The magnetic field cone makes the ions rotate faster than the isochronous field would and consequentlytheir phases move closer to zero.

Dutto and Craddock, 7th Intl. Conf. on Cyclotrons, (1975) p. 271.

Gordon and Marti, Part. Acc. 11 (1980) 161.

Orbit Center Movement in the Central Region

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0.3

0.2

0.1

0.0

-0.1

-0.2

0.1

-0.2

-0.1

0.0

0.10.0-0.1 -0.1-0.2 0.0 0.1

g10g9

g5

g6

g8

g10 g8g4

g5

g7 g9

g7

g4

g3

g6

g2g3

g1g1

g2

+ +

2 in the non-relativistic approximation 2 E= Kinetic energy

1 1 2 22 2O

pp qB p mEqB

m E m E m E Ep p m E pqBm E E E m E

EE

ρ ρ

ρω

ρ

∆= ⇒ ∆ = =

∆ ∆ ∆ ∆∆ = ∆ ∆ = = ⇒ ∆ = =

∆∆ ∝

Motion of the Orbit Center at Higher Energies

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0.0

0.0

-1.0

-1.0

1.0

1.0

x and y in inches

We can see in this graph that shows the motion of the center of curvature on the 10th turn of the K500 central region that the effects of the gaps are a lot less noticeable, and the dominant effect is the hill to valley motion. The flutter has already developed quite strongly.

After 10 turns we have gone through 60 energy gains at the gaps.

Note that the scale is of the order of inches, not tenths of inches.

The rotation is due to the spiral.

Ion Sources for Cyclotrons

Internal sources– Internal ion sources in cyclotrons were utilized from the very beginning.– They are convenient because they don’t require much additional hardware– But they are limited to low charge states

External Injection– Injecting the beam from outside the cyclotron allows the utilization of a larger

volume source but requires additional hardware: transport line, inflector, etc. Typical examples of these sources are the ECRs utilized at MSU.

– Two basic types of external injection:• Radial - The beam is injected in the midplane of the cyclotron through a hole in the

yoke, example MSU K1200. An electrostatic deflector or a charge stripper are utilized to capture the beam in an accelerated orbit.

• Axial - The beam is injected along the central axis of the cyclotron and bent into the median plane by a device (inflector), example MSU K500.

I will describe the additional hardware, the details of the ion sources themselves are treated in the ion source lecture.

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Examples of Internal Ion Sources

Left drawing: internal PIG source used at LBNL 88” cyclotron (room temperature magnet)

Right photo: Internal source used in commercial cyclotron (Ionetix) with superconducting magnet.

Notice the difference in size: cross section in median plane ~ 30 mm vs 3 mm

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Axial Injection into a Cyclotron

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InflectorA strong field exists in the central axis hole of a superconducting cyclotron that focuses the beam. A major issue is the very large fringe field that affects the beam even before it turns vertical

Field on the Axis of a Superconducting Cyclotron

The very large increase (0.1 5 T) in the axial field along the central hole produces a large focusing of the beam

The transverse phase space ends with a small (~ 1 mm) diameter beam but with a large transverse momentum

The inflector at the center of the cyclotron has to be able to accept this beam and transfer it into the median plane with no losses.

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Median plane

Bottom of the yoke

Injection into a Cyclotron: Electrostatic Mirror

The electrostatic mirror was the first inflector used in cyclotrons and very simple to build

A major disadvantage is that the beam must pass twice through the grid with the corresponding losses in transmission

The beam sputters the grid and it must be frequently replaced, specially with heavy ions

Used for many years at LBNL and many other laboratories

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Median plane

HV electrode

Grounded grid

Beam enters

Beam exits

Cyclotron axis

Injection into a Cyclotron: Spiral Inflector

The spiral inflector originally proposed by Belmont and Pabot soon displaced the electrostatic mirror as the inflector of choice. It basically consists of two electrodes that create an electric field shaped to have the field perpendicular to the orbit. It is more difficult to calculate and construct but there are no grids to damage and need very little maintenance.

The photos above show the MSU K500 inflector developed in 1986

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More on Inflectors

Spiral inflectors come in all sizes. The photo above shows the TRIUMF spiral inflector in a very low field cyclotron

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Although the beam is injected on the axis of the cyclotron, the non-zero emittance phase space implies that some of the ions in the beam will move on a helical orbit around the axis, traversing a larger path than the central ray of the beam. This longer path produces a debunching of the beam due to the magnetic field in the central hole of the cyclotron. The figure above shows the efficiency drop for a ±5 and a ±20 degrees acceptance of the central region. This simulations are for first harmonic operation. In higher harmonics the effect is more pronounced because the same path length represents a larger number of RF degrees.

Why do we need a stripper?

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Stripping is obtained by intercepting the beam with a thin media at some intermediate energy in the accelerator chain The emerging charge will depend on the media material, its thickness and

the projectile energy. Final energy in a cyclotron is proportional to Q2.

• p=QeBρ» Qe is the ion charge» where B is the average magnetic field at extraction» ρ is the extraction radius» E α p2 α Q2 but only one charge state can be accepted

In a linear accelerator the final energy is proportional to Q.• E=V*Qe• More than one charge state can be accepted for acceleration

The cost of the accelerator can be lowered by increasing the charge Q

Q1 Q2

Stripping Injection in Coupled Cyclotrons: MSU CCF

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K500Rextraction = 66 cmHarmonic = 2ωRF=2 ωorb

K1200Rinjection = 33 cmHarmonic = 1ωRF= ωorb

ωorb at extraction = ωorb at injection => vext = vinj (Rext/Rinj)~3 vinj

Same RF frequency in both cyclotrons

Rinj~33 cmRext~100 cm

Radial Injection by Stripping

Injection into MSU K1200 Cyclotron

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Stripping foil inside dee

Dipole-Quadrupole

Focusing Barneeded to compensate defocusing effect of magnet edge field

Closed orbit after stripping

Incoming beam from K500 Bad environment for the

stripper!!!

Inside a dee (~150 kV)In the vacuumIn a 5 T magnetic fieldHigh radiation level

Stripper inside K1200 cyclotron

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Carbon Foil: short lifetime for heavy ions

Simple hardware: a rotating wheel with a large foil allows to deposit high power without exceeding temperatures ~ 1800 C

The problem is that the heavy ions with high flux produce a “flattening” of the foils, interpreted as the effect called “ion hammering” that changes the thickness of the foil in the direction of the incident beam.

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Foil thinning displaces the peak of the stripped beam charge distribution toward lower charge states. Foil thickness measured with α source.

Magnetic Field

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What are the requirements for the magnetic field?– In the classical cyclotron the midplane magnetic field Bz should increase as γ(r)

to maintain isochronism (ion rotation in sync with RF system fixed frequency)

– 𝝎𝝎 = 𝒒𝒒𝒒𝒒𝒎𝒎𝒐𝒐𝜸𝜸 𝒓𝒓

𝒒𝒒𝒊𝒊𝒊𝒊𝒐𝒐𝒊𝒊 = 𝜸𝜸 𝒓𝒓 𝒒𝒒𝒐𝒐 = 𝒒𝒒𝒐𝒐𝟏𝟏𝟏𝟏−𝜷𝜷𝟐𝟐

= 𝒒𝒒𝒐𝒐𝟏𝟏

𝟏𝟏 − (𝒓𝒓𝝎𝝎𝒊𝒊 )𝟐𝟐

But this increasing field with radius creates problems.

As we can see in the figure, the vertical force experienced by an ion rotating clockwise (seen from above) is restoring, toward the median plane, if the B field decreases with radius

Magnetic Field Focusing

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Vertical focusing : – Magnetic field locally defined by power law

– 𝒒𝒒𝒛𝒛(𝒓𝒓) = 𝒒𝒒(𝒓𝒓𝒐𝒐)(𝒓𝒓𝒓𝒓𝒐𝒐

)𝒌𝒌 𝒓𝒓𝒐𝒐 𝒌𝒌 = 𝒓𝒓𝒒𝒒𝒛𝒛

𝒅𝒅𝒒𝒒𝒛𝒛𝒅𝒅𝒓𝒓

– �̈�𝒛 − 𝝎𝝎𝟐𝟐 𝒌𝒌 𝒛𝒛 = 𝟎𝟎 𝝎𝝎𝒛𝒛 = −𝝎𝝎𝟐𝟐𝒌𝒌 νz = 𝝎𝝎𝒛𝒛𝝎𝝎𝒓𝒓𝒓𝒓𝒓𝒓

= −𝒌𝒌

– νz is the axial betatron frequency (the motion is stable for k < 0)

– In an isochronous field B~ 𝛽𝛽, 𝑞𝑞~𝛽𝛽 , 𝒌𝒌 = 𝜷𝜷𝜸𝜸𝒅𝒅𝜸𝜸𝒅𝒅𝜷𝜷

~ 𝜸𝜸𝟐𝟐 − 𝟏𝟏 vertical motion is unstable

Radial focusing : – It can be shown that the radial motion betatron frequency is given

by

– νr = 𝝎𝝎𝒓𝒓𝝎𝝎𝒓𝒓𝒓𝒓𝒓𝒓

= (𝟏𝟏 + 𝒌𝒌) ~ 𝜸𝜸

– With the radial motion being stable for k > -1

Alternatives: Thomas Cyclotron, Hills and Valleys

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Maximum energy (1937)

Bethe and Rose, Phys. Rev. 1937, v. 52, p. 1234.

Rose, Phys. Rev. 1938, v. 53, p. 392.

Hill to valley, decreasing field, but Vr is negative.Valley to hill, increasing field, but Vr is positive. The forces are restoring in both cases

Sector Focusing

When entering a hill from a valley there is an outward pointing component of the velocity (Vr)that combines with the forward pointing azimuthal field (Bθ) providing a restoring force. Both components reverse when leaving the hill.

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Vertical cut along an azimuthal circle

Spiral Sectors

Introducing spiral sectors produces a radial component of the B field (Br) that in combination with the azimuthal velocity Vθ contributes a vertical force (qBθVr). This force is focusing when entering the hills and defocusing when leaving, providing net focusing according to the strong focusing principle.

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Bz

Br Br

Focusing with Spiral Sectors

The flutter factor is defined as:

𝐹𝐹2= 𝑞𝑞𝑧𝑧2 − 𝑞𝑞𝑧𝑧

2

𝑞𝑞𝑧𝑧2

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• Increasing the magnetic field in a superconducting magnet reduces the flutter.

• Increasing the number of sectors reduces the flutter

The vertical focusing frequency is

ν𝑧𝑧2 = −𝑑𝑑𝑞𝑞𝑧𝑧

𝑑𝑑𝑞𝑞𝑧𝑧𝑑𝑑𝑑𝑑

+ 𝐹𝐹2 1 + 2 𝑡𝑡𝑡𝑡𝑛𝑛2𝛿𝛿

Even though increasing the number of sectors reduces focusing, there are reasons for doing it. Avoiding resonances and increasing the number of RF structures (located in the valleys)Similarly with increasing the magnetic field, it reduces the size of the magnet.

Extraction From the Cyclotron

The beam extraction together with the injection are probably the two more complicated processes in the operation of a cyclotron and during the design process of a new accelerator. The problem is specially difficult in a high beam power cyclotron and/or a very high magnetic field machine. The main issue is the proximity of the orbits at the extraction radius.

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Cyclotron Extraction

Extraction by stripping No stripping

Non resonant extraction by acceleration Resonant extraction

Precessional extraction

Borrowed extensively from: W. Joho, Thesis 1970, SIN.

Extraction by Stripping

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Advantages:1. Used mostly in H-

cyclotrons for radioisotope production although it can be used for heavy ions

2. The fringe field is crossed very fast for H-

H+ stripping3. The extraction energy

can be changed by moving the stripper to a different radius

4. Multiple simultaneous energies

Stripping Extraction: TRIUMF H-

The simplest extraction system is to use a charge stripper (but emittance may suffer). The beam is sent though a thin foil (usually a carbon foil):

– When accelerating negative ions, the ion changes the sign of the charge (H-

H+) reversing the curvature of the orbit and leaving the confinement of the magnetic field (example below TRIUMF K500 H- cyclotron)

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Extraction from the TRIUMF K500 cyclotron (3 beamlines shown)

The most common application of stripping extraction is the extraction of H- ions in radioisotope producing cyclotrons. These accelerators normally run very high currents and the extraction with conventional methods (electrostatic deflectors) is difficult because of the high power in the beam. Any losses could damage the deflector septum.

It gives the possibility of extracting simultaneously several different beams (even energies!).

The magnetic field is seen as an electric field in the reference frame of the H- ion and can produce the Lorentz dissociation of the weakly bound electron. The neutral particle is then lost from the beam

Heavy Ion Stripping Extraction: DUBNA U400 A classical example of the extraction of heavy ions by stripping is the Dubna U-400

cyclotron. We can see that the radius of extraction varies with the ratio of Qextracted/Qaccelerated.

In this case the beam energy has to be high enough for the equilibrium charge after passing through the foil to be significantly different from the accelerated charge.

An additional problem is that for heavy ions not all the ions are stripped to the same charge state. There are beam losses.

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Sector magnets

Extraction by Acceleration

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In this method we just used the turn separation available due to the energy gain. Remember that the turn get very close together at extraction.

Extraction with Electrostatic Deflectors

An electrostatic deflector is used to give the ions a kick toward larger radii. It is a thin sheet (septum) (typically ~ 0.25 to 0.5 mm) in front of a high voltage electrode at a negative potential. Typical electric fields are of the order of 100 kV/cm

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Extracted orbit

Last internal orbit

Ideal case: separated orbits

High voltage cathodeGround septum

Ions

Electric field

Thermal simulations of the beam loss in the K1200 deflector septum

Homework: Turn Separation

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2 2 2 4 2 2 2

2

2

22

2

Starting from the equations:

and show that to first order in

the following equation applies:

22

or in general

rr

p c m c mc mc KineticEnergy mc TTp qBr

mc

dTdr dTmc

Tr Tmc

ε γ

νν

= + = = + = +

=

= =

21

1 r

dr dTr T

γγ ν

=+

Extraction by Acceleration

The necessary turn separation for insertion of the septum can in some cases be achieved simply from the radius gain between orbits due to the energy change. The radius and energy gain are related by:

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21

1 r

Tr rT

γγ ν

∆∆ =

+

This equation tells us that to obtain a large ∆r we should

1) build a large cyclotron (proportional to r). It is more costly.

2) provide a large ∆T (energy gain per turn). Requires more RF systems and power, voltage holding might be an issue.

3) Extracting on the edge of the field (where Nur is smaller) we also contribute to the increase in ∆r. The phase slip on the edge will limit how far we can go. High energy gain helps here too.

γ is determined by the energy, so we can not change it…

Advantages of the Ring Cyclotron

The ring cyclotron combines all these effects to improve the extraction situation.

The magnetic field is concentrated in separated sector magnets. The region between the magnets has very weak (and reversed sign) field. This decreases the average magnetic field and increases the average radius needed to achieve a certain rigidity.

In the free space between sectors several large RF cavities can be inserted that provide large energy gain. They also provide space for robust extraction elements that are not limited in space by the small gap inside sectors.

But it is significantly more expensive

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PSI Injector II. 72 MeV protons. 99.97% effic.Average field 0.330.36 TVoltage 125250 kV, # of cavities 2 (+2 flattop)

Simulation of Multiturn Extraction by Acceleration: MSU K1200

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8.2

8.4

8.6

8.8

9

9.2

9.4

9.6

-55 -45 -35 -25 -15

E (M

eV/u

)

126127128129130131max"0"132133134

Initial phase Φo (deg)

37

37.5

38

38.5

39

39.5

40

40.5

41

41.5

-55 -50 -45 -40 -35 -30 -25 -20 -15 -10

R (in

)

126127128129130131max"0"132133134sept

Initial phase Φo (deg)

must

Precessional Extraction

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Integer resonance Nur=1: Precessional extraction

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r

1

For medium energy cyclotrons crosses 1 smoothly near extraction.It can be shown that if a first harmonic imperfection of amplitude b ispresent, this resonance crossing induces a coherent oscillat

ν

1

ion amplitude:

where is the effective duration (number of turns)

1of the resonance crossing .

If changes 0.05 per turn for example, then is approximately

c eff eff

effr

r eff

bx R t tB

tddt

t

π

ν

ν

=

=

rr

4.5.After crossing the resonance the orbit precesses. Looking at the beam once per revolution at fixed angle, the beam is rotating

1around the reference orbit with a frequency (1- ). It takes (1- )

νν

r

Precession r

1Precession r

turns

to complete a revolution. The angle is then 2 (1- ). The radius increment is

R 2 sin 2 sin (1- )2

Finally:

1R 2 sin (1- )

c c

r

x x

bRB d

dt

α π να π ν

π π νν

∆ = =

∆ =

EnergyNur=1

Nur

α

∆R

pr

xc

Precessional Extraction

To overcome the issue of the close proximity of neighboring turns we add an imperfection (first harmonic) in the magnetic field that induces precession in r-pr space.

We use the νr = 1 resonance

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R

pR

Differential probe trace in K1200 cyclotronSimulation of extraction in K1200 cyclotron

Extraction System of the K1200 MSU Cyclotron

The beam extraction in a high field superconducting cyclotron is a very complicated process involving magnetic field perturbations to the internal field, electrostatic deflectors and focusing bars.

The fringe field in the magnet produces a strong defocusing effect on the almost one full turn that the beam traverses in it.

A set of “focusing bars” (quadrupoles made of passive steel bars) compensate for that defocusing but at the same time produce strong perturbations in the internal field. We must introduce “compensating” bars that cancel the lower harmonics of these perturbations.

At the same time all the “holes” on the yoke produce perturbations that must be compensated with more holes.

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Magnet Hill High voltage electrode“DEE”

Injection Extracted beam

Passive Focusing Bars

The fast decaying fringe magnetic field in the superconducting cyclotrons produce a strong vertical defocusing force on the beam during an almost full turn during the extraction path

The passive focusing bars utilize the magnetization produced by the fringe field to generate a quadrupole field that keeps the beam from blowing up vertically during extraction.

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Field gradient obtained from POISSON for external fields of 8, 10, 12 and 30 kG (K500 MSU cyclotron)

B (kG)

x (inches)

beam

Space Charge Forces in Cyclotrons

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++

The force from the other ions increases the energy of the ions in the head of the beam

The force from the other ions decreasesthe energy of the ions in the tail of the beam

Higher energy

Lower energy

High Voltages can be Obtained in Large RF Cavities

In separated sector cyclotrons with large space in between the magnets it is common to use resonant cavities. They provide higher voltages (750 kV) and consume less power than dee systems, more efficient.

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PSI cavities

PSI 590 MeV is the Highest Power Cyclotron

The PSI cyclotron has been upgraded over a period of several years by improving the RF cavities.

The maximum current extracted (for constant beam loss) has been increasing following a law proportional to the inverse of the third power of the number of turns.

The energy spread generated by the space charge is proportional to the beam current I* N2 (N= total number of turns)

In addition another factor of 1/N is due to the fact that the turn separation at extraction is also proportional to 1/N

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References

Figures have been freely borrowed from many of the publications below G. H. Mackenzie, P. W. Schmor and H. R. Schneider, Encyclopedia of

Applied Physics, Vol. 4. Cyclotrons, 1992. M. K. Craddock, High Intensity Circular Proton Accelerators, TRI-87-2, 1987 M. Seidel, Introduction to Cyclotrons, 2012,

https://indico.gsi.de/event/1910/contribution/16/material/slides/0.pdf R. Baartman et al, THE TRIUMF 500 MeV CYCLOTRON: PRESENT

OPERATION AND INTENSITY UPGRADE, 2003 H. G. Blosser and D. Johnson, Focusing properties of superconducting

cyclotron magnets, NIM 121 (1974) 301.

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https://indico.gsi.de/event/1910/contribution/16/material/slides/0.pdf

The cyclotron as seen by … (David Judd)


PHY862 Accelerator Systems�CyclotronsContentMain Stages in the Evolution of the CyclotronBasic RelationsEnergy GainRF Harmonics: Example: 2 90o DeesSmooth Acceleration ApproximationThree Main Regions in a CyclotronCentral Region: K500 Example with Spiral InflectorHistorical Note: Electrolytic Tank AnalogueVertical Focusing in the Central RegionElectric Focusing: Changing StrengthDetails on the Electric Vertical FocusingOrbit Center Movement in the Central RegionMotion of the Orbit Center at Higher EnergiesIon Sources for CyclotronsExamples of Internal Ion SourcesAxial Injection into a CyclotronField on the Axis of a Superconducting CyclotronInjection into a Cyclotron: Electrostatic MirrorInjection into a Cyclotron: Spiral InflectorMore on InflectorsWhy do we need a stripper?Stripping Injection in Coupled Cyclotrons: MSU CCFRadial Injection by StrippingStripper inside K1200 cyclotronCarbon Foil: short lifetime for heavy ionsMagnetic FieldMagnetic Field FocusingAlternatives: Thomas Cyclotron, Hills and ValleysSector FocusingSpiral SectorsFocusing with Spiral SectorsExtraction From the CyclotronExtraction by StrippingStripping Extraction: TRIUMF H-Heavy Ion Stripping Extraction: DUBNA U400 Extraction by AccelerationExtraction with Electrostatic DeflectorsHomework: Turn SeparationExtraction by AccelerationAdvantages of the Ring CyclotronSimulation of Multiturn Extraction by Acceleration: MSU K1200Precessional ExtractionInteger resonance Nur=1: Precessional extractionPrecessional ExtractionExtraction System of the K1200 MSU CyclotronPassive Focusing BarsSpace Charge Forces in Cyclotrons High Voltages can be Obtained in Large RF CavitiesPSI 590 MeV is the Highest Power CyclotronReferencesThe cyclotron as seen by … (David Judd)

Felix Marti Michigan State Universityostroumo/MSU/Lectures... · 2018. 10. 11. · Felix Marti....

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