• Particle detectors: electrons, ions, photons, atoms

• Position detection

• Particle energy analysis

• Electron and ion detectors and energy analyzers

• Limitations of coincidence measurements

• Time-of-flight methods

• Examples

Preparation of atoms, molecules, ions, and photons

• Faraday cups

• Microchannel plates

• Position sensitive detectors

• Electron energy analyzers

• Mass spectrometers

• Time-of-flight

Particle detectors

Charged particles: Faraday cup

+-

60 V

+-

60 V

Biased cup

Cup with repellerelectrode

Electrometer

Electrometer

Ion / electron beam

Ion / electron beam

Bias potential prevents escape of secondary electrons from the cup, which would lead to a wrongmeasurement (higher current forions, lower current for electrons)

Neutral particles: surface ionization detector

Tungstenfilament

Bias potential(300 V)

Nozzle

Ion current

Heating

Collector

Atoms are ionized on thehot filament surface and collected.

Very efficient, if theionization potential (atom) is lower than thework function (surface)

Works well with:Heavier alkali atoms(K, Rb, Cs) / tungsten:Langmuir-Taylor detector

Secondary electron multipliers

Channeltron Microchannelplate (MCP)

1 kV

Primary particle(ion, electron, photon, fast neutral)

Channeltron: gain up to 108

MCP: gain up to 105 at each stage

Imaging detectors

1D: resistive layer anode:

x = d*QA/(QA+QB)

x

d

MCP

Anode

2D: wedge & strip anode:

Two coordinates can be reconstructed

Electron cloud charge is collectedand flows as a current pulse

Imaging detectors: delay line anodeDelay line anode:

t0

t1t2

x0

Dt = t2 - t1

x0 = Dt / c*

Resolution: time1 ns, length100μmdead time: 10-15 ns

•Two overlaying wire („spiral“) windingscollect the charge pulse. •The pulses propagate through thewire towards both ends.•Arrival times („delays“) are measured.

hexagonal delay line anode:

• Detect two (or more) electronswithout dead-time

Multi-hit: dead time limitation

stripes with no positioninformation due to dead time

for subsequent hits region with no positioninformation due to dead time

for subsequent hits

1st hitstandard delay line anode:

Time overlapping particles cause ambiguity

Fast multiparticle imaging detector

Review of Scientific Instruments 71 (2000) 3092

(decay time: 50 ns)(closingtime: 2 ns)

Time resolution: 0.4 ... 2 ns@ ∆t = 2 ... 30 ns

From the time-integratedCCD signals In

1, In2, Ig

1, Ig2

the time delay ∆t can becalculated

Analyzers for charged particlescharge: qmass: mvelocity: venergy: W = ½mv2

momentum: p = mv

Total energy: Wtot = Wkin + Wpot = (p-qA)2/2m + qU

Electrostatic potential U Electric field E = -grad(U) Coulomb force FC = qE

Vector potential A Magnetic field B = rot(A), Lorentz force FL = q(vxB)

Wien filter (velocity filter)

EF qC =

)( BvF ×= qL

E

B

BE

FF =⇒= vLC

v > E/B

v < E/B

E x B field configuration

Time-of-flight (TOF) spectrometer

vdt = mEv kin /2=Time of flight

dv

• Requires start signal (pulsed beams)• Good resolution at low energies• Works also for fast (keV) neutral particles

Ekin

v

Detector

Drift tube

Pure drift mode: velocity spectrometer.For high particle energies (mostly monochromatic beams of singlespecies: electrons, molecular ions in storage rings).

Dispersive spectrometers for charged particles

Projectile beam

Spectrometerwith detector

Target: atomic/molecular beam

)( BvF ×= qL rmv

Z

2=F

Magnetic spectrometer

Detector

particlesource

qBmvr =

B ⊗r

Decelerating field

I

UB Ee

dI/dU

Electrostatic spectrometers

UB0V

Grids

Ee

ϑz

Deflection in an electrostatic analyser

ϑ

z 0=ϑd

dz

45°

Usp

Ui= 0 V

0=ϑd

dz1st Order focusing:

0=n

n

dzd

ϑ

ϕ

Pass energy: spkin UfE ⋅=

f : Spectrometer factor – depends on the geometrytypical values: f = 1 – 2.

nth Order focusing:

Focusing in ϑ (2nd order) and ϕ (all orders)

ϑz

ϕ ϕ

Energy resolution:

limited by imaging properties, fringing fields

up to 2π solid angle acceptance in ϕ

02.0...001.0=ΔEE

Cylindrical mirror spectrometer (sector)

180° spherical spectrometer

Toroidal spectrometer

up to 2π solid angle acceptance in ϕ

Angular resolved photo electron spectroscopy (ARPES)

Mattauch-Herzog combines electrostatic + magnetic and magnetic deflectionE: monochromatic beam (E = const), B: momentum filter (mass filter)

energy: E = ½mv2 momentum: p = mv = (2mE)1/2

magnetic deflection: r = p/qB; E/q = constantr = (2m/q*E/q)1/2/B

Mass spectrometers

resolution ∆M/M≈10-5

Reflectronsecond spatial focus

electrostatic mirror

first spatial focusion source

detector

•Time-of-flight measured → mass information•Electrostatic mirror with harmonic potential refocuses ions•Used for studies with atomic and molecular clusters, and heavy molecules → very high mass resolution

Quadrupole mass spectrometer (QMS)

• Radiofrequency applied to the four rods let ion trajectoriesoscillate. For certain m/q values trajectories are stable and passthe filter• Typical residual gas analyzer (RGA), compact fieldinstrumentation for gas analysis

“Single collision“ experiments

Gas target

Projectile beam

Spectrometerwith detector

~~~

~~

--

+

~~~

-

H atom

H. Ehrhardt, Freiburg 1969

Coincident (e,2e) measuremente+H→H++e+e

•Experiments since the 1960s•Requirements:

•Crossed beams (projectile and target) •Detectors for low-energy electrons and ions

• Free metal atoms are excitedby electron impact

•Incident electron energy and spin are controlled

• Angle and energy dependenceof the scattered or ejectedelectrons

• Polarization and intensity of decay photons are determined

A modern “Franck-Hertz” experiment

Quantum scattering amplitudes and relative phases describing the interaction are determined to test theoretical models

Limitations of conventional spectrometers

Ion impact

b) 1 GeV/u U92+ p = 4.5·108 a.u., v = 110 a.u. (relativistic)

a) 5 MeV/u p+ p = 26 000 a.u., v = 14 a.u.

mEp 2=mpv =

510−=Δpp

9102 −⋅=Δpp

→ changes in projectile trajectory are not measurable!

Atom

p0pa

prec

ϑΔp

Double ionizationAtomp0

pa

pbpc

321321021221

5εεεσ eff

TD ENjdEdEddd

dN ΔΔΩΔΩΔΩΩΩΩ

=

Toroidal spectrometer(Université Paris XI)

seV

mmnA

eVcmND

1002.03101010010 261122

222 =⋅⋅⋅⋅= −−

−+− +→+ eHeHee 32

Electron gun

Count rate:

one hit every 10 min!

Main problem: small solid angle

Statistical limitations

Time-of-flight and position:full momentum informationLarge acceptance (up to 4π):multicoinicdence

Imaging spectrometers

Gas-Jet

Ions

Electrons

Projectile

E-Field

E-Field

Ion trajectory Position-sensitivedetector

• Detection of ions and electrons• Developed (ca. 1985) for target ion spectroscopy

• Recoil-Ion Momentum Spectroscopy (RIMS)

• Cold Target Recoil-ion Momentum Spectroscopy (COLTRIMS)

gas jet

Helmholtz-coils

drift tubes

spectrometer plates

projectile beam

recoil detector

electron detector

Reaction Microscope

Recoil ion carries kinematic information

ion electron

Projectile mass m

vfc

(backward)

vfP

(forward)Recoil

Reaction microscope

E|| : longitudinal kinetic energy of ionsm : massq : charge state

TOF:⎥⎥⎦

⎤

⎢⎢⎣

⎡

++

±+⋅=−+

qUE

d

EqUE

amEt||||||

||/

22

)(

Separation of different q/m

Longitudinal ion momenta: from TOF

+Uo

a d

A

+U = Uo/2

ion trajectory

detector

+

-

+Uo

a

A

+U = Uo/2

ion trajectory

detector

+

-

r

qUdamt )2(

2+= m

pv ⊥

⊥ =2

)2( damqUp

r += ⊥

Transverse ion momenta: from position

Time focusing condition: d = 2a

TOF

/ µs

a / cm

Gas jet

d = 22 cm

+Uo

a d

rAr++

Ar: vjet ≈ 550 m/s

All particles in the gas jethave the same velocity vjet

r(Ar+) = 2.4 cmr(Ar2

+) = 3.4 cm

Ar+

Ar2+

p(Ar) = 18 a.u. p(Ar2) = 36 a.u.::p(Ar1000) = 18000 a.u. => Ekin = 60 eV

0 50 100 150 200 2500

50

100

150

200

250

X Axis

Y A

xis Ar+

Ar2+

Ar++

1 cm

0 50 100 150 200 2500

50

100

150

200

250

X Axis

Y Ax

is

0 50 100 150 200 2500

50

100

150

200

250

X Axis

Y A

xis

0 20000 40000 60000 800001

10

100

1000

10000

100000

coun

ts

time-of-flight [ns]

Ar+

Ar2+Ar++

H2O+

H2+

Ar+

Ar2+

Ar++

Detector imageall ions

Detector image only Ar++

Condition

Positions at detector• Particles having different momentaarrive after ionization at different times and positions on the detector• Time or position conditions can be set to choose one type

Electron spectrometer

Cyclotron motion:

Fcentrifugal = FLorentz

mv⊥2 / R = q.v⊥

.B

p⊥ /R = q.B

Radius : R = p⊥ /(q.B)

Frequency: ω = q.B/m = 2π/T

Projectilebeam

Detector

B-Field

r

R

v ⊥

Target

•A weak magnetic field keeps theelectrons close to the drift axis•Energetic electrons cannotescape detection

B = 10 Gauss

m = 1/1836 (Electron)p ⊥ = 2.7 a.u.(Ee = 100 eV)

R = 3.3 cmTw = 35 ns

m = 4 (He+ ion)p⊥ = 2.7 a.u. (EHe = 13.5 meV)

R = 3.3 cmTw= 260 ms !

Multiple revolutions

Less than one revolution!

R

v⊥

Example: photoionizing He

R

v⊥

Side view

B-Field y

x

ϕ

X

p⊥

R r

ωt ϑ

Reconstruction of electron momenta from position ( r ,ϑ ) and TOF (t)

View onto detector plane

|sin(ωt/2)| = r/(2R)

R= r / (2.|sin(ωt/2)|)

from R = p⊥ /(qB):

p⊥ = r.q.B / (2.|sin(ωt/2)|) Needed: field strength B

Emission angle: ϕ = ϑ – ω t/2

Position rR = const; (same p⊥)

Different TOF:(different p||)

If t = N.T (N = integer number)then r = 0 independent of R for all p⊥ (magnetic focusing)

Ee = 0 eV

10 eV

50 eVT

T = 26 ns

B = 13.46 Gauss

6 revolutions

Electron emission spectrum: position vs. TOF

Charge exchange betweena highly charged ion and an atom

recoil ion charge state

14 3 2

projectile charge state

Xe41+

5

Xe40+

Xe39+

single capture

true triple capture

true double capture

single autoionisation

Charge exchange Xe42+

Single capture: scattering angle vs. Q-value

n = 13 14 15 16 17 n = 14 15 16 17 18

• Capture of the electron into high Rydberg states of the projectile• The ionization potential of the target affects the final state• Scattering angle depends on the principal quantum number n• Lower n means that the projectile has aproached the targetnucleus more, and the scattering angle is therefore larger

Q value (arbitrary units) Q value (arbitrary units)

Sca

tterin

g an

gle

(mra

d)

End 19.10.2011

Additional information on

counting statistics

Conditions for Poisson distribution:

1) The events are uniformly and randomly distributed over the sampling intervals

2) The probability of detecting an event during an infinitesimaltime interval dt is ρdt, where ρ is the expected counting rate.

3) The probability of detecting more than one event during the infinitesimal time interval dt is negligible ρdt « 1.

If the events are counted over a finite time period, dt, with an average probability ρ, with μ= ρdt, the Poisson distribution, P(N), describes the probability of recording N counts in a single measurement:

Detector counting statistics

!)(

NeNP

N μμ −

=

If the measurement is repeated a large number of times and the values of N are averaged, the average value of N approaches the mean of the distribution, μ, as the number of repeated measurements approaches infinity.

The Poisson distribution has a standard deviation σN

NN ≈= μσ

Detector counting statistics

Gaussian vs. Poisson distribution

For a large number N, the Poisson distribution can be approximated by a Gaussian one.

Two different distributions usually appear in a counting experiment:

1) The number of counts in a given channel follows a Poisson/Gaussian distribution (counting statistics)

2) The width of the experimental signal in channels depends on the detector resolution. The line shape very often follows a Gaussian distribution. The centroid of this second Gaussian distribution is assumed to be close to the “true” value.

Gaussian distribution: 5% and 95% confidence limits

Gaussian distribution

Counts N in a selected region of a Gaussian peak (or area of this region).

σN% for selected values of N.N σN%

1 100.0%100 10.0%10,000 1.0%1,000,000 0.1%

Percent standard deviation σN% = relative standard deviation σN / N divided by 100%

The centroid of a Gaussian peak can be determined with an error of: N

FWHMc 35.2

=σ

Gaussian distribution

-100 -50 0 50 100 1500

100

200

300

400

500

600

700

Weighting: y No weightingχ2/DoF = 90.4833R2 = 0.99798y0 0.22617 ±1.22184xc 0.78041 ±0.09602w 37.15415 ±0.21655A 29870.24314 ±180.12

Model: GaussWeighting: y Statisticalχ2/DoF = 0.36303R2 = 0.99713y0 0.0041 ±0.09716xc 0.627 ±0.10023w 37.09159 ±0.15315A 29822.74766 ±155.86

B Gauss fit of Data1_B

num

ber

of c

ount

s

Difference in count numbers

Results of a counting experiment

χ2 : (sum of the squares of observed values – expected values)/ divided by the expected values

Size of sampling interval required to determine the position of the Gaussian peak to a certain accuracy

Maximum systematic centroid error due to an asymmetricalignment of the sampling interval relative to the true centroidof the Gaussian peak.

Size of sampling interval in multiples of FWHM

Maxim

um

cen

tro

iderr

or

(% o

f FW

HM

)

A continuous analog signal can be reconstructed exactly from discrete digital samples by employing a universal interpolation function, provided the sampling frequency, 1/Ts, exceeds twicethe maximum frequency contained in the analog signal.

This requirement is the Nyquist limit for avoiding aliasing of higher frequencies to a lower frequency.

Nyquist limit

Aliasing: the redcurve is wrong!

Not enough samplesto reconstruct theblue curve

• The dominant error in determining the centroid and area of a peak is the random error from statistics.

• The systematic error due to the size of the sampling interval becomes negligible compared to the random error if the sampling interval is half as broad as the peak FWHM (or less).

• The shape of the lines has to be Gaussian or otherwise defined. To make sure that this is the case, a much narrower sampling interval may be needed.

Error estimates in counting experiments