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