Non-radioactive radiation sources - Universitetet i Oslo · Non-radioactive radiation sources ......
Transcript of Non-radioactive radiation sources - Universitetet i Oslo · Non-radioactive radiation sources ......
Non-radioactiveradiation sources
FYS-KJM 4710
Audun Sanderud
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X-ray tubeD
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• Electrons are released from the cathode (negative electrode) by thermal emission – accelerated in an evacuated tube – hit the anode (target, positive electrode) – bremsstrahlung is generated:
X-ray tube and radiationD
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• Target and filament, mostly tungsten• X-ray radiation: in fact denoting all photon generated from electrons slowing down
• Power P=V x I; unit kW• Radiation yield:
Energy out as X-ray radiation/Energy inn ~ 0.1% – 2%
for 10keV – 200keV electrons (increasing with kinetic energy) in tungsten
X-rays – direction characteristicD
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• Direction of the emitted photons dependent mostly of electron energy:
Kramers rule 1)D
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• Unfiltered (energy fluence-) spectrum is given from Kramers rule:
T0-3ΔT T0-2ΔT T0-ΔT T0-hνmax Photon energy, hν
Rad
iate
d En
ergy
, R
´(h ν
)
T0 T0-ΔT T0-2ΔT T0-3ΔT T0-4ΔT 20 e
rad
col
When T <m c :dT const.dxdT 1dx T
⎛ ⎞ ≈⎜ ⎟⎝ ⎠
⎛ ⎞ ∝⎜ ⎟⎝ ⎠
Kramers rule 2)D
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• Kramers spectrum: R´(hν)=CNeZ(hνmax-hν)
Differential radiant-energy spectral distribution of bremsstrahlung generated in the thick target of atomic number Z, hνmax=T0 , is the maximum photon energy.
Dependents of Dependents of the atom number the X-ray potential
hν=T0 hν=2T0 Photon energy
R´(h
)
Photon energy
R´(h
)
2Z1
Z1
2kV1
kV1
Filtering and the X-ray spectrumD
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• Filtering modify the spectrum, both in intensity and characterization
FilterAttenuation coefficient µThickness x
• Each photon is attenuated with a probability e-µx, where µdepend of energy and filter medium
• Low energetic (“soft”) X-ray radiation attenuated most• X-ray spectrum is more homogenous with more “hard”filtering
X-ray spectrum Example Fig 9.10D
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• X-Ray spectrum from 100-keVelectrons on a thick tungsten target
0
2
4
6
8
10
12
14
16
0 20 40 60 80 100 120
hv, keV
Rad
iant
ene
rgy
spec
trum
, Arb
. Uni
ts Unfiltered
0.01mm W
2mm Al
0.15mm Cu and 3.9mm Al
20m Air
SpectrometryD
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• Measurement of radiation spectrum• Pulse- height analysis by:
- Scintillation counter, (NaI(Tl)):Light is emitted at irradiation – intensity (“height”) of light pulse proportional with quantum energy – number of pulses at each pulse height gives intensity of the given energy interval
- Semiconductor (Ge(Li)):Current pulse trough p-n- junction at irradiation – height of pulse proportional with quantum energy. Best, but most be cold with liquied N2
X-ray spectrumD
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• Example: 100 kV voltage, 2.0 mm Al-filter• Average energy ~ 46 keV
Dashed: Exposure
Solid: Fluence
X-ray quality D
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• X-ray spectra gives most detailed characterization• But: spectrometry is expensive, time demanding• Half value layer the recommended standard
minimum 50 cm, collimated field
Absorbent(aluminum or copper)
Air based ionization chamber with electrometer
HVL: thickness of absorbent which reduces the exposure (~absorbed dose to air) with 50 %
Half value layer - HVL
• Exponential attenuation of photons give:
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µHVL
eNNN
eNN
µHVL
µx
2ln2 0
0
0
=⇒
==
=
−
−
• X-ray quality is often given as half value layer in aluminum an copper
CyclotronD
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• Acceleration of charged particles which are kept in a circular motion.
• Two part D-structure
• Time dependent voltage between the two D
• Two accelerations per cycles - period synchronized with voltage
• No good principle for acceleration of electrons an other light particles
v B
(t)EIon source (z>0)
Cyclotron – description 1)D
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• Particles is rotated 180º with a B-field, but accelerated by a time depending potential (kV/MHz)
• Potential V gives:
• Combined with the Lorentz force:
2 21 2T=zV= mv v2
zZm
⇒ =
- Stronger magnetic field; larger ability of acceleration
- Radius increases with mass
(F=zv×B)
222
22
2
mv zBrF =zvB=ma= vr m
2zV zBr 2mVrm m zB
⎛ ⎞⇒ = ⎜ ⎟⎝ ⎠
⎛ ⎞= ⇒ =⎜ ⎟⎝ ⎠
Cyclotron – description 2)D
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• The period Γ of a charged particle I a circular motion is:
2πr zBrΓ= , v= v m
2πm Γ=zB
⇒
• Γ is then independent of the speed but:
• m is relativistic mass and increase with the speed:
m = γm0 , γ = (1-β2)-½ , β=v/c
Cyclotron – description 3)D
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• When the speed increase will the period Γ increase
• Conservation of energy (Tb and Ta: kinetic energy before and after acceleration):
( )( ) ( )
2a b 0
2 2a 0 b 0
a b 20
a 0 0b 2
0
T =T +zV , V= E×dl , T= γ-1 m c
γ -1 m c = γ -1 m c +zVzV γ =γ +
m c
2πγ m 2πm2πm zV Γ= γ + zB zB zB m c
⇒
⇒
⎛ ⎞⇒ = = ⎜ ⎟
⎝ ⎠
∫
Cyclotron – description 4)D
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• Rise in period proportional with zV/m0c2
• Example: zV = 100 keV
• Proton: zV/mpc2 ~ 0.01 %
• Electron: zV/mec2 ~ 20 % → close to 50 % rise in one round → Time dependent E-field will have the wrong direction in relation to movement of the electron
• The E-field frequency can be synchronized with the rise in period → synchrocyclotron / synchrotron
Linear-accelerator 1) D
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• Acceleration of charged particles in strong microwave field (~ Ghz):
Linear-accelerator 2) D
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• Effective acceleration potential ~ MV
• Electron gets close to light speed after acceleration in one cavity
• Electron can hit a target (ex. Tungsten) – high energetic bremsstrahlung generated
Acceleration tubeEffective potential: 6MV
cavity
Acceleration tubeD
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• Standing waves makes the electron “surf” on a wave of the electric field
• The amplitude decide the effective acceleration potential
Photon spectrumD
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• Different characteristic than from the X-ray tube
11.3 MeV electrons against 1.5 mm tungsten target. Lines: models of variation thickness of the target
BetatronD
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• Charged particle (electron) accelerated in doughnut shaped unit:
• Time dependent magnetic field used to accelerate the electron and to make the electron move in a circle
MicrotronD
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• Acceleration in resonator – circular orbit with magnetic field; combination of linear accelerator and cyclotron
• Correlation between growth of radius and period