Physics with many positrons:positron sources and positron beams

The problem :

Many-positron experiments in matter need bunches of 10³ or more e+within ca. 0.2 ns on spots of ca. 100 nm

NEPOMUC, the most intense current e+ source, delivers

ca. 1 e+/ ns ( 100 pA ) into a spot of 7 mm FWHM

( at E = 1keV , D E = 50 eV , B = 10 mT )

Compression required : in space by 5 , in time by 4 orders of magnitude

A possible solution : further upgrade of the NEPOMUC / Scanning PositronMicroscope ( SPM ) facility at Munich

SPM at FRM-II:

• up to 106 events / second

• Reduced measuring time (factor 50, ca. 1 h / picture)

• improved lateral resolution (≤ 1 μm)intended: 50 - 100 nm lateral resolution

G. Kögel : Remarks on particle optics

( Phase space, paraxial optics, aberration correction, bunching, remoderation )

Case study of the Munich Positron Microscope

( Various beam lines, remoderation stages, application ofoptical principles in design and construction,outlook to many positron pulses )

Ch. Hugenschmidt : Positron sources, positron beams

W. Egger : Applications of pulsed positron beams

Remarks on particle opticsRay tracing : determine by finite element methods E(r) and B(r),

Then solve d²r/ dt² = q ( E(r) + v x B (r) ) ; v = dr/dt

Crossing of trajectories in real space is confusing

Representation in Phase Space x i , p i = d L ( x k , v k ) / d v i , i,k = 1,2,3. . Then Liouville´s Theorem holds : D x Dp x = W x = const ; DE Dt = W E = const

A beam is defined by W = const ; Trajectories never cross in phase space

A beam is completely described by the energy E, intensity I, W x , W y , W z.

Brightness B = I E / ( W x W y ) = positrons / ( source area x solid angle )

Exercise : Which energy spread do you expect, if the cross section of theNEPOMUC beam was shrinked to the necessities of multi positronexperimentation ?

Solution : W x W y =d² ( Dp )² = d² DE trans / 2m+ = 1 cm² x 50 eV /2m+

At d = 100 nm we get from Liouville`s Theorem

D E (at experiment ) = 500 GeV

Spatial focussing : The force should increase linearly with distance to axis

Perfect Solution : Quadrupole

E x = c x ; E y = - c y or B x = b x ; B y = - b y

⇒Strong focussing in y- directionstrong defocussing in x–direction

Quadrupole optics ideally suited for a line focus

For a spot, one needs at least two quadrupoles in seriesexpensiveSo far not applied for keV positron beams

Round lenses

Coaxial sets of tubes, cones, …where E and B have rotational symmetry

E r = - r/2 dE z / dz + r³/16 d³E z / dz³ + … ( also for B )

In the paraxial approximation to the equ. of motion, only linear terms contribute:

Same equ. for y(z). If there is a B-field, the x- and y- axis rotate around the z-axis by an angle Q(z) defined by

dQ /dz = qBz /2mvz ( rotating system ).

Only in the rotating system the x- and y- motions are independent ! In the lab system, positrons entering the B-field parallel to the z-axis from a field-free region gyrate around this axis with azimuthal angle Q (z) !

In the par. approx., any solution is a linear combination of two principal rays( linear differential equ. of 2.order ). This is the foundation of linear optics.

0)(4

)(2)(0

2

02

2

0 =−

++⎟

⎠⎞

⎜⎝⎛ − x

zUU

zBmq

dzUd

dzdxzUU

dzd z

A typical electric lens with the twoprincipal rays

The focal lengths f 1 , f 2 and thepositions of the foci dependstrongly on the potentials. Theydefine the optical properties.

Magnetic single pole lens withmagnetic field lines

Standard magnetic lens

Note : The radial fields at entrance and exitcounteract. => least aberrations for a focusclose to the maximum of E z

Liouville´s theorem and paraxial optics

Source paraxial system focal spot

2 a s 2 a f

D s , Dp s , E s D f , D p f , E f

D f = D s D p s / D p f => D² f = D² s ( a² s E s ) / ( a² f E f )

Note : The minimal spot size is always close to a focus. For an image, the beam must expand again, until each resolved pixel has ~ the sizeof the focal spot. This simplifies our task.But a f is limited by aberrations because of the third and higherorders in the expansion of radial focussing fields

Spherical aberrations

Disk of least confusionslightly before the paraxialfocus

Focus location : field free region close to field maximum magn.lenses of SPMAberrat. Const C s > 10 f C s ~f C s = 0.4 f

⇒Even under the most optimistic assumptions, the present NEPOMUC beamcan not compressed to a spotsize below 2 mm

Scherzer´s Theorem (1937) : With only round lenses and no space chargebetween trajectories and the axis , the spherical aberration is always positive.

6focus

2S

focus||,

source||,2focus

2source2

source2min 4

ααα C

EE

dd +=

Feasibility of aberration – corrected positron beam systems ?

In electron microscopes, corrections by sextupoles and multipoles of higherorder have been achieved eventually, after 60 years of failures.

Since for multi-positron experiments the spot sizes are orders of magnitudelarger than in electron microscopes, and since we need no image of thesource, the correction by the induced charge in grids is feasible withoutintolerable perturbation by the meshes of the grid

Correction by space charge:The main deflection is due to a magneticlens ( not shown ). The positronsexperience only outward directedcorrection forces

Also correction by multipole optics could beconsidered

Compression in the time domain : bunching

Liouv. Theor. => D t (bunch) > D t D E / D E (bunch)

Because of aberrations, D E (bunch ) < E / 10⇒T drift > 20 D t

L drift > 40 D t [ ns ] ( E [ keV] ) ½ [ cm ]

The voltage at the buncher gap, U(t), must change rapidly :dU / dt = D E / D t (bunch ) = 10 …. 100 V/ns

Usually the buncher is part of a rf circuit operated in resonance

D E (bunch)

Buncher types

Coaxial resonator

( Q ~ 100 , L = 1.5 m at 50 Mhz )

Double gap buncher,

Q ~ 300 – 1000

Disadvantages of resonant (sine wave ) bunchers

Only ca. 10 % of a continuous beam arebunched, 90 % produce background

Available options :1. Sawtooth prebuncher ( SPM )

U ~

U~

Up to 70 % in bunch

2. Storage trap / harmonic prebuncher

Slow e+ ( 0.2 mm/ns at 100 meV ) are collected for µs and releasedby suddenly switching to theharmonic potential

Beam chopper : Removal of the unbunched background

U(t)

open

t

a= 2 U(t) l / (Uc w)

Typically : pulse FWHM 3 ns , rise time of U (t) ~ 1 ns , amplitude 2V

The fringing fields at the entrance to and exit from the chopper platesmodulate as well the longitudinal beam energy since the exit of thepositrons is delayed relatively to the entrance by the transit time v/l of thepositrons !

w

End of the tutorial introduction into fundamentals of particle opticsand functional elements of the Munich positron beams

Conclusion

Without new tools from outside the range of traditional particle optics, there is no chance for true multi-positron experiments, at least at NEPOMUC .

Remoderation, The key concept of positron particle optics

W

Re-emitted positrons constitute a narrow , pulsed source with energy spreads in the few kT range ( details depending on material, surface properties and vacuumconditions ). The ( more intense) backwards emitted beam must be separatedfrom the parent beam.The easily extracted beam in forward direction (transmissionmode) depends on very thin ( ~ 100 nm ) remod. crystals.

crystal effic. ( reflexion ) cleaning technique further remarksW(100,110) ~ 20 % ~ 2500 K in UHV very reliable ( > 10 years) Ni(100) ~ 30% sputtering, H2 -n-SiC ~ 60% uncleaned, 10 y in air energy spreads unknown

Summary on particle optics in relation to positron experiments

Phase space considerations give us a reliable, simple insight into thefeasibility of a project or the usefulness of existing parts.

Numerical simulations ( ray tracing )are only needed for the optimization of critical components, e.g. spot forming lenses.

The main handicap of positron beam physics is the low brightness of allpositron sources (when compared to electron sources)

This is partially compensated by remoderation of positrons. Also correctionof spherical aberration should be more efficient and less expensive as in electron optics.

To remove the enormous adiabatic heating of the beam due to thecompression in an ( optical ) beam system , a sequence of remoderationstages is necessary for spots / pulses in the sub µm / sub ns region. Thisintroduces dramatic losses in intensity. There is an urgent need forcoordinated research into better and more efficient moderators .

Case study of the Munich SPMG.Kögel

Positron beam systems consist of those components discussed in the previouslecture. The necessary functional parts are arranged in series and thepositrons are transferred by beam lines

Source line 1 comp. 1 line 2 / / line n comp. n exper. Area

The components are separately designed ( existing parts, advisers, numericalsimulations ) for the least possible expansion of effective phase space volume.

Also the beam lines are important for the conservation of the effective phasespace volume.

About beam lines

A) Free propagation B) Periodic lens sequence

C) ( Longitudinal ) magnetic guiding field

Gyr. freq w g = qB/mGyr. length L g =2p v/ w gAdiabatic invariantM = R²g B ~ constIf variation of B is low overdistances R g , L g

⇒Adiabatic scaling R g ~ B-1/2

⇒Gyration energy ~ B⇒Energy conservation couples longi-

tudinal and transverse motion

More about magnetic beam transport : Correction coils and beam bends

To steer the beam use long weak dipole fields. Positronsfollow adiabatically the slightly tilted field lines.Short dipoles ( kickers ) introduce a collective gyration. Dueto the velocity dispersion Dv after a distance

L = L g v/Dv the diameter will increase from d toD = d + 2 R g !

bends need a transverse saddle coil field B = mv/qR

pulse duration is increased by d / F v

Main disadvantage of magnetically guided beam lines

For cylindric symmetry, the canonical momentum p f is a constant of themotion which couples transverse and longitudinal motion in the fringingfields at the transition from the magnetic field into field free sections.

p f = m r² d f / dt + q B r² / 2

Example : positrons are emitted ( e.g.from a moderator ) parallel to fieldB start at distance r start to the axis . Thenp f start = q B start r² start / 2

After extraction from the field ( B=0) at distance R from the axis

R df / dt = v trans = (q/2m) B start r² start / R

And the transverse kinetic energy has changed from zero to

E trans = m v² trans /2 = ( w g r start )² ( r start / R )² / 4

Example : NEPOMUC beam , R = r start = 4mm, B = 10 mT deliversE trans = 140 eV , or aperture a = 0.27 at 1 keV beam energy

Influence of fringing fields and symmetry breaking by a ferromagnetic terminator

A) Without terminator : theLorentz- force of the entireflux deflects the positrons

B) With terminator : the B – field is constantup to the N ferromagnetic vanes. The Lorentz – force is reduced by a fatcor ~ N .

60 mm

Field terminator for NEPOMUC beam. The vanes are from amorphos FeSiB(B sat =1.5 T, yield strength ~ 1GPa )25 µm thick, 2mm apart.The corpus is shaped from µ-metalwith µm tolerances where required

Beam lines for positrons : a critical assessment

Type => free propagat. lens sequence magnetically guided

advantagesLow aberrationoptic actionpossible

expensive, first adjustmentboring, for good beamsonly

Simply adjustet, works evenunder suboptimal adjustment,enables cheap bends, tolerates external magn fields

Strong aberrations unlessentrance and exit are properlyterminated. Quantitative simulation is demanding

Long-distance transfer lines,

table-top beams with sourceand target in the field

deficiencies

In positronbeamsystemsrecomendedfor

Remoderated beamsMicrobeams, diffraction,…..

No phasespacedeformat.. Cheap

for verygood beamsonly

Beam diagnostics

Diagnostic units distributed along the beam system accelerate the tediousadjustments considerably. In magnetic beam lines , simple devices (shownbelow) are well suited . Channel plates are more expensive and bulky. They also tend to distort the actual field distributions.

beam

retarding field grids , removable

aperture , removable

transverse energy spread from var. of energy distribut. with Bz

Bz

Remoderation in reflection

Electrostatic. Reduction of source diameterby a factor of up to 10

Remoderator of the Munich SPM with magnetic single pole lensand magnetic dipole field for theseparation of primary and remoderated beams. Reduction of source diameter by a factor of ~100.

The inset presents the hollowpole tip , the axial magneticfield and the remod. location. Inside the pole tip, themagnetic field decreasesrapidly . For large beam spotsthis is a better location !

Scanning Positron Microscope (SPM)

Moderator-chamber

Saw-tooth-buncher(50MHz)

Sine-buncher(100 MHz)

Accelerator5 keV

Beamswitch

Remoderator

Last buncher(100 MHz)

+ Blanker

Single-pole lens

Accelerator1-20 keV

Single-pole lens

Scan-coils

Electron-gun

Specimen-chamber

DetectorPhys.Rev.Lett. 87,067402 (2001)Nature 412, 23 August 2001, 764

source: < 30 mCi

energy: 1-20 keV

pulsing: 50 MHz

time-window: 20 ns

count-rate: 500 / s

timeresolution: 250 ps

peak / BG: 103

beam-spot: ≥ 2 μm

recording-time

XY scan:

week(s) !

The Munich SPM in the original version

Pre-buncher, blanker, main buncher

Beamswitch

• Function: magnetic prism

Incoming beam:E = 5keV, parallel displacement

Remoderated beam:E≈200 eV, deflection by 45°

PulsingPre-buncher

Blanker

Main-buncher

Last-buncher

PULSING

SPM : optical column for positron lifetime images at 1 – 30 keV beam energy

Magnetic single-pole lens

SPM: lateral resolution

Optical image

Indentation in GaAs: • beam energy 16 keV; mean implantation depth 550 nm; resolution 2 μm; step-size 2.5 μm;• two lifetimes in the centre: 70% with 365 ps ⇒ vacancy clusters

Schematics for the interface NEPOMUC / SPM

Interface NEPOMUC / SPM

Magnetically guided sectionfor puls formation at 20 eVbeam energy.

The magnetic field isterminated by a ferromagnetic grid

The resonator coil is locatedoutside the vacuum systemfor rapid change to lowerbuncher repetition rates i.e. more positrons per bunch.

Advanced reflection remoderator

Because of the expected progressat NEPOMUC, the single pole lens is equipped with twoconcentric pole shoes and excitation coils. Withoutdeterioration of sphericalaberrations, the focal length canbe varied between 8 and 16 mm.

For the remoderated positrons, a field lens is included

Positron elevator , a Linac tailored for keV positron microbeams

The microbeam gains 10 keV potential energy withnegligible increase of theenergy spread.

The elevator is a modifieddouble gap buncher of high Q (~ 5000 ) in whichthe static potentials arearranged so that bothgaps are fieldfree whenthe positrons cross them.

In the future, by means of positron elevators both the source and thespecimen stage can be operated at ground potential.

SPM: Positron Elevator

Summary on the status of SPM

Both the intended time resolution ( ~ 0.2 ns ) and spot size ( ~ 2µm ) have beenachieved without an intense source

Ca. 95% of the components for implementation at NEPOMUC are manufacturedWith the exception of the positron elevator, all functions have been succesfullytried and testet at NEPOMUC

Transfer and implementation at NEPOMUC are expected in 2010

Outlook to possible multi-positron experiments at NEPOMUC/ SPM

The SPM was designed for single-positron experiments. Further components areneeded for multi-positron experiments. The best choice depends strongly on theactual improvements made by the upgrade to NEPOMUC II.Under optimistic assumptions, 10 k positrons / bunch could be achieved by a single harmonic buncher in the beam line, enough for studies in material science.

For more positrons / bunch, either a gas-moderated storage trap must bedeployed in the beam line, or the entire SPM must be relocated to an intensepulsed positron source, e.g. a high power LINAC with low repetition rate.

••

Upgrade for experimentswith many positrons ?

Harmonic buncher in beamline with / without furtherremoderation ?or / andgas-moderated trap ?

Experimentation stage :Ready for materialsscience. 60 mm windowfor access with laser light etc available. Furtherchanges need discussion.

Reduced rf ( 12.5 Mhz) in 1. column ?

Acknowledgement

Over the past two decades about 50 scientists and students havecontributed to the progress of positron beam physics at Munich.

The colleagues mentioned below are also standing for the othercolleagues from the respective groups :

W. Triftshäuser, K.Schreckenbach, R.Brusa

D.Schödlbauer, P.Sperr, A. David, D.T. Britton, K. Uhlmann

W.Egger, Ch.Hugenschmidt, Ch. Piochacz

Funds were provided by (among others ) the European Union, theFederal Republic of Germany, the Free State of Bavaria, theDeutsche Forschungsgemeinschaft and the Universities at Trento , Munich ( TUM) and Neubiberg (UniBwM) .