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An Introduction to the IonAn Introduction to the Ion--Optics of Optics of Magnet SpectrometersMagnet Spectrometers

U. Tokyo, RIKENU. Tokyo, RIKENThe 14The 14thth RIBF Nuclear Physics SeminarRIBF Nuclear Physics Seminar

Series of Three LecturesCNS, University of TokyoFebruary 27, 2006

Georg P. BergUniversity of Notre Dame

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The LectureThe LectureSeriesSeries

11stst Lecture: 2/27/06, 10:30 am: Formalism of ionLecture: 2/27/06, 10:30 am: Formalism of ion--optics and the optics and the design of a complete systemdesign of a complete system

22ndnd Lecture: 2/27/06, 1:30 pm: Magnet design, systems and diagnostiLecture: 2/27/06, 1:30 pm: Magnet design, systems and diagnosticscs

33rdrd Lecture: 2/27/06, 3:00 pm: Experiments with dispersion matched Lecture: 2/27/06, 3:00 pm: Experiments with dispersion matched high resolution spectrometers high resolution spectrometers

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22ndnd LectureLecture

• Review 1st Lecture (4)• Overview magnetic elements (5)• Creation of magnetic fields B (6 - 9)• Design and examples of dipole magnets (10 -16)• Quadrupole magnets, doublet, triplet (17 – 20)• Spectrometers (21 – 24)• Wien Filter (25)• Diagnostics considerations (26)• Field measurements (27 - 30)

• Electro-magnetic elements in ion-optical systemsDipoles, Quadrupoles, Multipoles, Wien Filters

• Combining elements, ion-optics properties• Diagnostics and field measurements

22ndnd Lecture: 10/7/05, 2:00 pm: IonLecture: 10/7/05, 2:00 pm: Ion--optical optical elements, properties & designelements, properties & design

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Review 1Review 1stst LectureLecture

Lorentz Force: (1)

Xn = R X0TRANSPORT of Ray X0

using Matrix R

(3)

R = Rn Rn-1 … R0

TRANSPORT of σ Matrix (Phase space ellipsoid) σ 1 = Rσ0 RT

ε = √⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯σ11σ22 - (σ12) 2 (5)

Taylor expansion, higher orders, solving the equation of motion,phases of a separator project

(4)

Beam emittance:

(10)

Schematic Overview of Magnetic Elements (Iron dominated)Schematic Overview of Magnetic Elements (Iron dominated)

G. Schnell, Magnete, Verlag K. Thiemig, Muenchen 1973

Iron dominated:

B field is determined byproperties & shape of ironpole pieces

FieldPole shape wIPole,analyt. Bx

Power ~ IPower ~ I2 2 ~ R~ R44 Required wI = Ampere-turnsfor desired magnet strengthB0, g, a3, a4 can be calculatedformula in last column.

Coils are not shown in drawingin 1st colunm

Creation of magnetic fields using currentCreation of magnetic fields using current

Current loop Helmholtz coil, Dipole

Helmholtz coil, reversed current,Quadrupole

Magnetization inFerromagneticmaterial:

B = μ H

B = magn. InductionH = magn. Fieldμ = magn. permeability

Biot-Savart’s Law

(16)

Creation of magnetic fields using Creation of magnetic fields using permanent magnetspermanent magnets

Magnet iron is soft: Remanence is very small when H is returned to 0 Permanent magnet material is hard: Large remaining magnetization B

Permanent magnets can be used to design dipole, quadrupole and other ion-optical elements. They need no current, but strength has to be changed by mechanical adjustment.

A few comments onA few comments on

Normal (NC), Super (SC) conducting, Permanent magnets (PM)Normal (NC), Super (SC) conducting, Permanent magnets (PM)

•• IonIon--optical elements can are optical elements can are areare built with all three methods: NC,SC and PM built with all three methods: NC,SC and PM

•• IonIon--optics is concerned with the fields and not how they are createdoptics is concerned with the fields and not how they are created. .

•• Magnet design is very different because of different technologiMagnet design is very different because of different technologies.es.

•• Fields in NC, SC (current driven) magnets can be easily varied,Fields in NC, SC (current driven) magnets can be easily varied, PM need mechanical changes.PM need mechanical changes.

•• Normal conducting coils are limited to typically 10 A/mmNormal conducting coils are limited to typically 10 A/mm2 2 (though 50 A/mm2 is possible)(though 50 A/mm2 is possible)

•• NC conducting need a lot of electrical power, SC much less, PM NC conducting need a lot of electrical power, SC much less, PM none.none.

•• Strong, current dominate SC magnets can be built (~ 5 Strong, current dominate SC magnets can be built (~ 5 -- 10 T).10 T).

•• Iron dominated magnets are limited by iron saturation ( < 1.7 Iron dominated magnets are limited by iron saturation ( < 1.7 –– 2.2 T).2.2 T).

•• SC need 4.2 K cryogenic and liquid Helium cooling (note: high tSC need 4.2 K cryogenic and liquid Helium cooling (note: high temp. SC improving) emp. SC improving)

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Magnetization CurvesMagnetization Curves

Field lines of H-frame dipole

Pure IronVanadium Permandur

SOFT IRONSOFT IRON

B(H) of SA08, INLC & SSM250 Low Carbon Magnetic Steel

0.0

0.2

0.4

0.6

0.8

1.0

1.2

1.4

1.6

1.8

2.0

0 10 20 30 40 50 60 70 80 90 100

Field Strength H / Oers

Indu

ctio

n B

SA08INLCSSM250

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Design of an ironDesign of an iron--dominated dominated Dipole magnetDipole magnet

Field lines of H-frame dipole

CoilNI

Gapg

⇑ Magnetic field B in Good-field region

defined by ion-opticalrequirement, e.g. dB/B < 10-4

For symmetry reasonsonly a quarter of the fulldipole is calculated & shown

The Field calculation was performedUsing the finite element (FE) codeMagNet (Infolytica). Other programsare TOSCA or POISSON.

NI (Ampere turns) = NI (Ampere turns) = ------------------------------------------------------B (T) B (T) ** g (m)g (m)

44ππ * * 10 10 ––7 7 (m/A)(m/A)

B

From AmpereFrom Ampere’’s law: s law:

Units: m = meterUnits: m = meterT = TeslaT = TeslaA = AmpereA = Ampere

Note: FE codes solve the static of time varying Note: FE codes solve the static of time varying MaxwellsMaxwells EquationsEquations numerically by numerically by ““meshingmeshing””the geometry in triangles in 2d or the geometry in triangles in 2d or ““bricksbricks”” in 3d. This allows to precisely calculate the in 3d. This allows to precisely calculate the FieldsFields(B,E) for any (B,E) for any configuraitonconfiguraiton of current and materials, like ferromagnetic metals of current and materials, like ferromagnetic metals

(17)

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SHARAQ SHARAQ Dipole D2Dipole D2

Iron-dominated, normal conducting Dipole Magnet with constant field in Dipole Gap (Good-field region)

• Soft magnet iron, B(H)• Hollow copper conductor

for high current density< 10 A/mm2

• Iron magnetization saturatesat about 1.7 T

• For B > 2 T superconducting(current dominated or hybrid) magnets are used.

30o Edge Angle Vertical Focusing

Dipole Gap: +/- 100 mm

60o BendAngle

Units in mm

Coil

Coi

l ReturnYoke

Central Ray

PolePiece

ReturnYoke

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SHARAQ Dipole D2 SHARAQ Dipole D2 Field calculationField calculation

Units in mm

These figures show theGood-field region in thecenter of the magnet andthe maximum field B as function of the current I in the conductor

CALCULATED B(I) CURVEcompared to linear approximation

0

0.2

0.4

0.6

0.8

1

1.2

1.4

1.6

1.8

2

0 500 1000 1500 2000 2500

Current I / A

Ind

ucta

nce

B/T

=

non-linearlinear

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Fringe field & Effective Fringe field & Effective field length field length LLeffeff

Leff = B ds / B0

2Leff

Pole length

Iron Pole

Note:1) The fringe field is important even in 1st order ion-optical calculations.2) Rogowski profile to make Leff = Pole length.3) The fringe field region can be modified with field clamp or shunt.

(18)

↓↓ EFB = Effective Field BoundaryEFB = Effective Field Boundary

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SHARAQ SHARAQ Dipole D2Dipole D2

Iron-dominated, normal conducting Dipole Magnet with constant field in Dipole Gap (Good-field region)

• Soft magnet iron, B(H)• Hollow copper conductor

for high current density< 10 A/mm2

• Iron magnetization saturatesat about 1.7 T

• For B > 2 T superconducting(current dominated or hybrid) magnets are used.

30o Edge Angle Vertical Focusing

Dipole Gap: +/- 100 mm

60o BendAngle

Units in mm

Coil

Coi

l ReturnYoke

Central Ray

PolePiece

ReturnYoke

RogowskiRogowski end profileend profile

PhysicalPhysicaledgeedge

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SHARAQ Dipole D2SHARAQ Dipole D2specifications and specifications and

Coil designCoil design

This figure shows the coil with hollow cupper conductor for water cooling ( 4.3 A/mm2 )

Units in mm

Thumb rule:Thumb rule:Water cooling Water cooling has to dissipate has to dissipate the complete the complete magnet power IRmagnet power IR22

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Dipole HDipole H--Magnet for St. George a new recoil Magnet for St. George a new recoil separator at Notre Dame University for astrophysicsseparator at Notre Dame University for astrophysics

Iron-dominated Dipole Magnet with constant field Bmax = 0.6 T in dipole gap (Good-field region).

Central Ray

Coil

Coil

ReturnYoke

PoleDipole Gap: +/- 30 mm

6o& 12o

Edge Angles Vertical Focusing

Units in mm

40o BendAngle

• Soft magnet iron, B(H)• Hollow copper conductor

for high current density• Iron magnetization saturates

at about 1.7 T, small returns

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Standard Standard QuadrupoleQuadrupole

Note: Magnet is Iron/Current configuration with field as needed in ion-optical design. 2d/3d finite elements codes solving POISSON equation are well established

Return Yoke

Current in & out of drawing plane

Pole Piece

Coilsin

out

N

S

in

out

out

in

S

N

x

y

in

out

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Forces on ionsForces on ions ( ( quadrupolequadrupole))

⇑

⇒

⇓

⇐

Horizontally defocusing quadrupolefor ions along – z axis into the drawing plane. See Forces ⇑⇐⇓⇒in direction v x B

Quadrupole Hexapole

A focusing quadrupole isobtained by a 90o rotation around the z axis

Octopole

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Ion optics of a Ion optics of a quadrupolequadrupoleSINGLETSINGLET

& & DOUBLETDOUBLET

VERTICAL

HORIZONTAL

DOUBLET

SINGLET

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Focusing with a Focusing with a quadrupolequadrupoleTRIPLETTRIPLET

Screen shot of TRANSPORT designcalculation of Quadrupole Tripletupstream of St. George target. Shownare the horiz. (x) and vert. (y) envelopsof the phase ellipse.

Note beam at Slit has +/- 2 mradand at target TGT +/- 45 mrad angle opening.

This symmetical triplet 1/2F-D-1/2F corresponds to an optical lens.

<- x ( +15 mm)

<- y +15 mm

z (8 m) ^^ Slit

1 mm

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K600 K600 SpectrometerSpectrometer

Bending radius ρ0 = 2.0 mBmax = 1.7 TGap = 5 cm (D 1), 6cm (D2)Weight = ~ 30 tons (D1)

~ 45 tons (D2)

Medium Dispersion: B(D1)= B(D2)Resolving power: p/Δp = 20000Dispersion = 12 cm/% ( = 12 m )Magnification Mx = 0.41Large range: Emin /Emax = 1.14

The K600 is shown in0o Transmission mode

High Dispersion PlaneB(D1) > B(D2)

Kinematic correction: K coilHexapole correction: H coil

IUCF K600,decommissioned IUCF K600,decommissioned In 1999, now in WS line RCNPIn 1999, now in WS line RCNP

iThembaiThemba Labs K600,Labs K600,South Africa in useSouth Africa in use

(x|(x|φφ22))

((x|x|ΘΘ22))

((x|x|ΘΘ))

3 dispersion modes 3 dispersion modes ((low,medium,highlow,medium,high) ) set by D2/D1 ratioset by D2/D1 ratio

lowlow

mediummedium

highhigh

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BIG KARL BIG KARL SpectrometerSpectrometer((JuelichJuelich, KFZ), KFZ)

Bending radius ρ0 = 1.98 mBmax = 1.7 TGap = 6cmWeight = ~ 50 tons (D1)

~ 70 tons (D2)

Resolv. power: p/Δp = 0 - 20600Dispersion = -2.0 to 26 cm/% Magnification Mx = 0.63 – 1.26Magnification My = 25.4 – 1.94Large range: Emin /Emax = 1.14Solid angle: < 12.5 msr

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BIG KARL Sample SpectraBIG KARL Sample Spectra

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Grand Raiden High Resolution SpectrometerGrand Raiden High Resolution SpectrometerMax. Magn. Rigidity: 5.1 TmBending Radius: 3.0 mSolid Angle: 3 msr

Beam Line/Spectrometer fully matched

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The The WienWien FilterFilter(1)

F = 0 when qE = qv x B with E ⊥ Β

v = E/B with E ⊥ Β

1,813kV/mm 0.3 T

B Field linesGradient of E Field lines

Units in mmElectrostatic system ofDanfysik Wien Filter

Design study of Wien Filterfor St. George

(19)

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Discussion of Diagnostic ElementsDiscussion of Diagnostic Elements

Some problems:

• Range < 1 to > 1012 particles/s• Secondary beam intensities typically up to 106 part./s• Interference with beam, notably at low energies • Cost can be very high• Signal may not represent beam properties (e.g. blind viewer spot)

Some solutions:

• Viewers, scintillators, quartz with CCD readout• Slits (movable) Faraday cups (current readout)• Harps, electronic readout, semi- transparent• Film (permanent record, dosimetry, e.g. in Proton Therapy)• Wire chambers (Spectrometer, secondary beams)

• Faint beam 1012 → 103 (Cyclotrons: MSU, RCNP, iThemba)

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Hall ProbeHall Probe

Hall Effect: UH = ⎯⎯ BI

Lorentz force ev x B on electrons with velocity v that constitute the current I

RH = Hall constant, material property

RHd (20)

Remarks:• Precision down to ~ 2 10-4

• Needs temperature calibration• Probe area down to 1 mm by 1 mm• Average signal in gradient field

(good for quadrupole and fringe field measurement)

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NMR ProbeNMR Probe

Nucleus with spin

Nuclear spin precessesin external field B With Larmor frequency

fL = ⎯ B2μh

μ = p, d magn. Momenth = Planck constant

fL (proton)/B = 42.58 MHz/T

fL (deuteron)/B = 6.538 MHz/T

(21)

Fig. 1

Principle of measurement:Small (e.g. water probe), low frequency wobble coil B + B~ , tuneable HF field B≈ (Fig. 1) with frequency ft , observe Larmorresonance on Oscilloscope (Fig. 2). When signal a & b coincide the tuneable frequence ft = fL

Fig. 2

• Precision ~ 10-5

• Temperature independent• Needs constant B in probe ( 5 x 5 mm) to see signal!

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Search Coil used in field map of S800, MSUSearch Coil used in field map of S800, MSUInduced Voltage Induced Voltage

in search coil in search coil U = U = -- dB/dB/dtdt

Coil is moved from outsideCoil is moved from outsideB = 0 T to inside B = 0 T to inside BBmaxmax

(calibrated with NMR probe)(calibrated with NMR probe)B at location (B at location (x,yx,y) is obtained) is obtained

by by intergrationintergration

S800 S800 Dipole D1Dipole D1

Ref: J. A. Ref: J. A. CaggianoCaggiano, Dissertation, NSCL MSU, 1999, , Dissertation, NSCL MSU, 1999, Spectroscopy of Exotic Nuclei with the S800 Spectrometer Spectroscopy of Exotic Nuclei with the S800 Spectrometer

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Field map of D2 of S800, MSUField map of D2 of S800, MSU

Ref: J. A. Ref: J. A. CaggianoCaggiano, Dissertation, NSCL MSU, 1999, , Dissertation, NSCL MSU, 1999, Spectroscopy of Exotic Nuclei with the S800 Spectrometer Spectroscopy of Exotic Nuclei with the S800 Spectrometer

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End Lecture 2End Lecture 2