preparation of atoms, molecules, ions, and photons › forschung › apix › ... · • electron...
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• 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