Beam Production, Characteristics and Shaping
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1 Beam Production, Characteristics and Shaping Dr. Manfred Sassowsky
2 Outline X-ray production 60 Co units Linear Accelerators Beam characteristics Beam shaping Beam Production, Characteristics and Shaping / / M. Sassowsky 2
3 Literature 1. E.B. Podgorsak (Technical Editor): Radiation Oncology Physics: A Handbook for Teachers and Students, IAEA, Vienna, 2005, ISBN , 2. TRS 398: Absorbed Dose Determination in External Beam Radiotherapy, IAEA, Vienna, H. Reich (Hrsg.): Dosimetrie ionisierender Strahlung, B.G. Teubner, Stuttgart, ISBN (out of print) 4. H. Krieger: Strahlenphysik, Dosimetrie und Strahlenschutz (2 volumes), B.G. Teubner, 2001, ISBN X and ISBN Recommendations of the Swiss Society of Radiobiology and Medical Physics ( Beam Production, Characteristics and Shaping / / M. Sassowsky 3
4 X ray production: Principle Heated cathode: AC voltage U H Thermoelectric emission of electrons Tube voltage U accelerates electrons towards anode Electrons interact with anode material (See lecture "Basic radiation physics") => X rays Kinetic energy of electrons: W = e U e.g.: U = 100 kv => W = 100 kev Cathode (heated filament) ~ U H e - e - e - e - e - e - e - U Vacuum X rays Anode Beam Production, Characteristics and Shaping / / M. Sassowsky 4
5 X ray production: Focussing In particular for diagnostic X ray beams: small spot size needed (higher image resolution) Focusing using guard electrode with Cathode (heated filament) Guard electrode voltage U f ; negative with respect to ~ U e - e - H e- cathode e - e - X rays e - Anode U f U Vacuum Beam Production, Characteristics and Shaping / / M. Sassowsky 5
6 X ray production: Efficiency Efficiency: η = k Z U Z = atomic number of anode material U = tube voltage k = constant; η = P P k 10 Radiation Electric 9 V 1 Numerical example: Z = 74 (Wo) U = 100 kv => η 0.01 i.e.: - only 1% of electron kinetic energy is transformed into radiation energy - 99% are dissipated in heat Technical challenge: cooling of anode => rotating anode Beam Production, Characteristics and Shaping / / M. Sassowsky 6
7 X ray production: Rotating anode tube Vacuum Dielectric cooling oil Cathode Anode Stator Rotor Focal spot Exit window Beam Production, Characteristics and Shaping / / M. Sassowsky 7
8 X ray production: Depth dose curve Relative Dose U < 100 kv: maximum dose practically at surface Depth in water (cm) Beam Production, Characteristics and Shaping / / M. Sassowsky 8
9 X ray production: Photon energy spectrum As discussed in lecture "Basic radiation physics" - Continuous X rays (Bremsstrahlung) - Characteristic X rays (Ionisation/excitation; subsequent photon emission) Relative Intensity W max = e U Photon energy Beam Production, Characteristics and Shaping / / M. Sassowsky 9
10 X ray production: Filtering Diagnostic applications: - Low energy photons to not traverse patient - Do not contribute to diagnostic image - But: lead to dose deposition => use of Cu and/or Al filters to decrease intensity of low energy photons Relative Intensity Increasing filter thickness W max = e U Photon energy Beam Production, Characteristics and Shaping / / M. Sassowsky 10
11 X ray production: Applications, Naming conventions Diagnostic - 2D images - Computed Tomography (CT) images => see lesson "Imaging for radiotherapy" Therapeutic - Superficial lesions - Not suited to treat deep seated tumours W = 10 kev kev W = 100 kev kev W > 1 MeV Superficial X rays Orthovoltage X rays Megavoltage X rays Beam Production, Characteristics and Shaping / / M. Sassowsky 11
12 60 Co units: 60 Co decay 60 Co decays to 60 Ni by beta-decay Half life t 1/2 = 5.26 years Excited state of 60 Ni de-excites to ground state by two subsequent gamma-decays Specific activity a: Activity per mass a = A m = N t A 1/ 2 ln 2 M A N A t 1/2 M = Activity = Avogadro s number = Half life = Molar mass Co 5.26 a 0.31 MeV β 1.17 MeV γ 1.33 MeV γ Ni a Bq/g (pure 60 Co) a Bq/g (technically achievable with 25% 60 Co) Beam Production, Characteristics and Shaping / / M. Sassowsky 12
13 60 Co units: 60 Co sources Source shape: pellets or disks 60 Co produced using neutrons from a nuclear reactor: 59 Co + n 60 Co + γ d = 1 cm... 2 cm Self absorption of gamma radiation in source: A eff l l x A x A μ μ da e = dx e = 1 l μ l 0 0 = ( μl e ) The longer the source, the higher the self absorption Typical values: μ cm -1 (disks), l 10 cm => A eff 0.25 A i.e. about ¾ of gamma radiation is absorbed in source Beam Production, Characteristics and Shaping / / M. Sassowsky 13
14 60 Co units: Shutter mechanisms Rotating cylinder Sliding drawer source W = Wolfram Ur = Uranium Pb = Lead source Operated by electromotor Safety mechanism: mechanical spring for emergency retraction Beam Production, Characteristics and Shaping / / M. Sassowsky 14
15 60 Co units: Treatment head Source Light bulb Fibre optic Primary collimator Secondary collimators Display of field size Depleted uranium Penumbra trimmer Lead Wolfram Beam Production, Characteristics and Shaping / / M. Sassowsky 15
16 Linear accelerators: Introduction Need for higher beam energies to treat deep-seated tumors Electrostatic acceleration limited to U 1 MV (discharges) => Use of particle accelerators Originally developed for research in elementary particle physics This lecture: only linear accelerators will be treated Basic idea: use moderate acceleration voltages many times to obtain higher total acceleration voltage Typical modern high energy linear accelerators (Linac): - Two photon energies (e.g. 6 MV, 18 MV) - Several electron energies (e.g. 6, 9, 12, 16, 20 MeV) Beam Production, Characteristics and Shaping / / M. Sassowsky 16
17 Linear accelerators: Electron gun: thermionic emission of electrons Accelerating waveguide: accelerates electrons using RF waves RF Generator Beam transport: transfer of electrons from accelerating waveguide to scatter foil or target Scatter foil: spreading of electrons for electron beams Target: generates photons from incident electrons Filter: flattening of photon beam Monitor chambers RF generator Power converters Stand Electron gun Overview RF Accelerating waveguide Scatter foil / Target + Filter Monitor chambers Gantry Beam transport Treatment couch Isocenter Beam Production, Characteristics and Shaping / / M. Sassowsky 17
18 Linear accelerators : RF Generation RF generator Electron gun Accelerating waveguide Beam transport Scatter foil / Target + Filter Monitor chambers RF Isocenter Power converters Treatment couch Stand Gantry Beam Production, Characteristics and Shaping / / M. Sassowsky 18
19 Linear accelerators: RF Generation (1) RF = Radio Frequency Used here as synonym for a high power, high frequency, electromagnetic wave Key element: Klystron High power RF amplifier Typical output: P 10 MW during Δt 5 μs f RF 3 GHz High voltage power supply charging Pulse forming network Klystron Low power RF pulse High power RF pulse Beam Production, Characteristics and Shaping / / M. Sassowsky 19
20 Linear accelerators: RF Generation (2) Klystron: Low power RF excites standing waves in 1st cavity Unbunched electron beam enters 1st cavity Bunching of electron beam: velocity modulation Drift region: bunch size decreases Bunched electron beam excites 2nd resonant cavity High power RF extracted from cavity Low power RF Cathode High power RF Resonant RF cavities Drift tube Anode Beam Production, Characteristics and Shaping / / M. Sassowsky 20
21 Linear accelerators : Electron gun RF generator Electron gun Accelerating waveguide Beam transport Scatter foil / Target + Filter Monitor chambers RF Isocenter Power converters Treatment couch Stand Gantry Beam Production, Characteristics and Shaping / / M. Sassowsky 21
22 Linear accelerators: Electron gun (1) Triode gun: pulsed electron bunches Thermoelectric emission of electrons (heated cathode) Anode voltage U positive with respect to cathode (15 kv kv) Grid voltage U g negative with respect to cathode (typ. 150 V) => Electrons can not pass grid, are kept in region between cathode and grid Cathode (heated filament) Accelerating waveguide Grid electrode Electrons Anode ~ U H U g U Beam Production, Characteristics and Shaping / / M. Sassowsky 22
23 Linear accelerators: Electron gun (2) Grid voltage U g set to zero during short time interval => Some electrons can pass grid, are accelerated towards anode Electron bunch Cathode (heated filament) Accelerating waveguide Grid electrode Electrons Anode ~ U H U g U g time U Beam Production, Characteristics and Shaping / / M. Sassowsky 23
24 Linear accelerators: Electron gun (3) Periodic pulsing of grid voltage Repeated electron bunches Cathode (heated filament) Accelerating waveguide Grid electrode Electrons Anode ~ U H U g U g time U Beam Production, Characteristics and Shaping / / M. Sassowsky 24
25 Linear accelerators: Acceleration RF generator Electron gun Accelerating waveguide Beam transport Scatter foil / Target + Filter Monitor chambers RF Isocenter Power converters Treatment couch Stand Gantry Beam Production, Characteristics and Shaping / / M. Sassowsky 25
26 Linear accelerators: Acceleration (1) Principle: use moderate acceleration voltages many times Explained using Wideroe accelerator (only of historical importance, but convenient to explain principle) Drift tubes, varying length L, alternating polarities Driven by RF Generator, frequency f RF, period T RF = 1 / f RF Acceleration of electron bunch in gaps between drift tubes AC generator ~ Gun L Drift tubes Beam Production, Characteristics and Shaping / / M. Sassowsky 26
27 Linear accelerators: Acceleration (2) AC generator ~ t = T 0 AC generator ~ t = T T RF AC generator ~ t = T 0 + T RF L Synchronicity condition: L = vt RF 2 Beam Production, Characteristics and Shaping / / M. Sassowsky 27
28 Linear accelerators: Acceleration (3) Modern linac: RF waves in accelerating waveguide - Travelling wave - Standing wave RF in RF out Travelling wave: - Hollow conducting cylinder as wave guide - Filled with discs (irises) Propagation speed (group velocity) of RF wave depends on geometry: - length of cells - Inner vs. outer diameter of irises Matched with electron speed 5 cm cm Beam Production, Characteristics and Shaping / / M. Sassowsky 28
29 Linear accelerators: Acceleration (4) Pictorial view: electrons ride close to the crest of the RF wave Bunch size is further decreased: - Faster electrons: advance experience lower accelerating field are thus brought back to bunch - Slower electrons: lag behind experience higher accelerating field are thus brought back to bunch V el V wave Beam Production, Characteristics and Shaping / / M. Sassowsky 29
30 Linear accelerators: Acceleration (6) RF forward RF reflected E Acceleration using standing waves End of accelerating waveguide is made reflecting for RF Forward RF wave is reflected back Superposition of forward and reflected RF wave yields a standing wave Maxima and minima of standing wave do not travel, but stay at fixed positions Beam Production, Characteristics and Shaping / / M. Sassowsky 30
31 Linear accelerators: Acceleration (7) More advanced standing wave structure with side coupled cavities Advantage: Can be made shorter than travelling wave structure (while obtaining the same electron energy) Beam Production, Characteristics and Shaping / / M. Sassowsky 31
32 Linear accelerators: Acceleration (8) Typical time structure of electron beam: Time Beam Production, Characteristics and Shaping / / M. Sassowsky 32
33 Linear accelerators : Beam transport RF generator Electron gun Accelerating waveguide Beam transport Scatter foil / Target + Filter Monitor chambers RF Isocenter Power converters Treatment couch Stand Gantry Beam Production, Characteristics and Shaping / / M. Sassowsky 33
34 Linear accelerators: Beam transport (1) Bend electron beam onto target Energy selection Charged particle in magnetic field: - Lorentz-Force: F L = q v B - Radius of curvature r : p r = qb q v p B = Charge = Velocity = Momentum = Magnetic induction Other magnet geometries are possible omitted here Beam Production, Characteristics and Shaping / / M. Sassowsky 34
35 Linear accelerators: Beam transport (2) Steering coils for fine-tuning beam position and beam angle Feedback from monitor chambers (explained later) Beam Production, Characteristics and Shaping / / M. Sassowsky 35
36 Linear accelerators : Scatter foil / Target + Filter RF generator Electron gun Accelerating waveguide Beam transport Scatter foil / Target + Filter Monitor chambers RF Isocenter Power converters Treatment couch Stand Gantry Beam Production, Characteristics and Shaping / / M. Sassowsky 36
37 Linear accelerators: Scatter foil (1) Left: Electron beam from accelerating structure is only a few mm in diameter ( Pencil beam ) Right: Treatment requires wide beams with a flat transverse beam profile S: Scatter foil scatters electrons to transform pencil beam into beam useful for treatment Beam Production, Characteristics and Shaping / / M. Sassowsky 37
38 Linear accelerators: Scatter foil (2) One scatter foil: limited transverse homogeneity and field size Energy dependence => Multiple scattering foils for high energy beams Additional ring shaped foils for low energy beams Beam Production, Characteristics and Shaping / / M. Sassowsky 38
39 Linear accelerators: Scatter foil (3) Homogeneous transverse beam profile but: - Energy loss - Energy straggling - Photon contamination from Bremsstrahlung Maximize scattering, minimise adverse effects => materials with high atomic number Z are preferred Beam Production, Characteristics and Shaping / / M. Sassowsky 39
40 Linear accelerators: Target / filter (1) Treatment with photons requires wide beams with a flat transverse beam profile Target Photons Filter Target: electrons interact with nuclei and emit photons (Bremsstrahlung); materials with high atomic number (Z) Filter: used to homogenise transverse beam profile; preferably materials with high Z Intensity distribution Collimator Beam Production, Characteristics and Shaping / / M. Sassowsky 40
41 Linear accelerators: Target / filter (2) Thin target Thick target Average photon energy Higher Lower Yield Lower Higher Electron stopper Yes No Cooling requirements Low High Target e - e - Electron stopper Target Filter Primary collimators Filter Primary collimators Beam Production, Characteristics and Shaping / / M. Sassowsky 41
42 Linear accelerators: Target / filter (3) Examples for different filter shapes a) Pb for low energies b) Pb or Wo for energies up to 15 MeV c) Fe with Pb core (25 MV Photons) d) Low Z (Al or steel) for high energies Beam Production, Characteristics and Shaping / / M. Sassowsky 42
43 Linear accelerators: Target / filter (4) Effects of filter on photon beam: Reduction of beam intenstiy in center of beam Reduction of total beam intensity Compton interaction and Bremsstrahlung => Decrease of photon energy Preferred absorption of low energy photons => Increase of average beam energy Contamination of beam with secondary electrons => Increase of skin dose Modification of depth dose distribution Photon energies above ~10 MeV: nuclear photo effect => Contamination of beam with neutrons Activation of materials in treatment head Beam Production, Characteristics and Shaping / / M. Sassowsky 43
44 Linear accelerators: Target / filter (5) Effects of electron-beam mis-steering a) Nominal beam b) Beam inclined c) Beam displaced d) Beam divergent Beam Production, Characteristics and Shaping / / M. Sassowsky 44
45 Linear accelerators: Target / filter (6) New approach: omit flattening filter Inhomogeneous open field Beam shaping with dynamic MLC (explained later) Higher dose rate in central part of beam 10X FFF 10X Beam Production, Characteristics and Shaping / / M. Sassowsky 45
46 Linear accelerators: Monitor chambers RF generator Electron gun Accelerating waveguide Beam transport Scatter foil / Target + Filter Monitor chambers RF Isocenter Power converters Treatment couch Stand Gantry Beam Production, Characteristics and Shaping / / M. Sassowsky 46
47 Linear accelerators: Monitor chambers (1) Monitor chambers measure: - Beam output in MU (monitor units) - Beam symmetry Calibrated so that 1 MU = 1cGy under defined conditions Transmission ionisation chamber - Two electrodes on HV (U) - Beam ionises air molecules - Charge separation in electric field - Charge (Q= I dt) => MU Beam I U Beam Production, Characteristics and Shaping / / M. Sassowsky 47
48 Linear accelerators: Monitor chambers (2) Located downstream of scatter foil / filter Two independent systems Each system: two sectors Differential signals => Beam symmetry => feedback to steering coils (explained earlier: beam transport) Beam Production, Characteristics and Shaping / / M. Sassowsky 48
49 Linear accelerators: Manufacturers Elekta Siemens Varian All manufacturers supply complete systems, i.e.: - Linac itself - Control system - Treatment table - Imgaging for patient positioning - Treatment planning software - Record + Verify software - Beam Production, Characteristics and Shaping / / M. Sassowsky 49
50 Beam Characteristics: Absorbed dose to water Absorbed dose is the deposited energy per mass: de D = dm SI unit is the gray (Gy): [ E] J [ D] = = = Gy [ m] kg 1 Gy = 1 Water is used as reference material (Properties similar to tissue, availability, physical properties well defined) J kg Beam Production, Characteristics and Shaping / / M. Sassowsky 50
51 Beam Characteristics: Depth dose photons (1) Percentage Depth Dose (PDD) curve of photons in water D surface D ex d max = Dose at surface = Dose at exit = Depth of dose maximum Build-up region D surface Depth in water Buildup region Beam Production, Characteristics and Shaping / / M. Sassowsky 51
52 Beam Characteristics: Depth dose photons (2) Increasing d max Percentage Depth Dose (PDD) curves of photons in water Source to Surface Distance (SSD) = 100 cm Photon beams ranging from 60 Co to 25 MV cm 2 field Increasing energy e.g.: 6 MV beam: d max 1.4 cm 18 MV beam: d max 3.0 cm Beam Production, Characteristics and Shaping / / M. Sassowsky 52
53 Beam Characteristics: Depth dose photons (3) Percentage Depth Dose (PDD) curves of photons in water Source to Surface Distance (SSD) = 100 cm 6 MV Photon beam Field size: cm 2 Increasing field size Beam Production, Characteristics and Shaping / / M. Sassowsky 53
54 Beam Characteristics: Depth dose electrons (1) Percentage Depth Dose (PDD) curve of electrons in water R th = therapeutic range R p = practical range R max = maximum range D skin D surface R 50 = depth where D rel = 50% (used as beam quality specification for electrons) Buildup region e.g. 6 MeV electrons: R 50 2 cm Bremsstrahlung tail Bremsstrahlung underground = R 50 Depth in water Beam Production, Characteristics and Shaping / / M. Sassowsky 54
55 Beam Characteristics: Depth dose electrons (2) Percentage Depth Dose (PDD) curve of electrons in water D rel 100 Electron energy ranging from 4 MeV to 30 MeV 50 Depth in water (cm) Beam Production, Characteristics and Shaping / / M. Sassowsky 55
56 Beam Characteristics: Transverse beam profile (1) Idealised transverse beam profile Relative dose as function of a transverse coordinate Transverse field size defined by Collimators / Blocks / MLCs ("beam shaping" - explained later) 100 D rel (%) 80 D Field size x Penumbra region Beam Production, Characteristics and Shaping / / M. Sassowsky 56
57 Beam Characteristics: Transverse beam profile (2) Real profiles Source to Surface Distance (SSD) = 100 cm 6 MV Photon beam Field size = cm 2 Depth = 1.5 cm 30 cm Increasing depth Beam Production, Characteristics and Shaping / / M. Sassowsky 57
58 Beam Characteristics: Transverse beam profile (3) Real profiles Source to Surface Distance (SSD) = 100 cm 6 MV Photon beam Depth = 1.5 cm Field size = 3 3 cm cm 2 Beam Production, Characteristics and Shaping / / M. Sassowsky 58
59 Beam Characteristics: Beam quality specification Superficial and orthovoltage X Rays: Half Value Layer (HVL) thickness Megavoltage X rays: Tissue to Phantom Ratio Q = TPR 20,10 = D 20 / D 10 Higher TPR 20,10 => more penetrating beam Electrons: R 50 SCD = 100 cm d = 20 cm D 20 D 10 Field size = cm 2 d = 10 cm Beam Production, Characteristics and Shaping / / M. Sassowsky 59
60 Beam Characteristics: Isodose distributions Isodose distribution: contours of equal relative dose Photons (6 MV) Photons (18 MV) Electrons (9 MeV) Electrons (20 MeV) Beam Production, Characteristics and Shaping / / M. Sassowsky 60
61 Beam shaping: Collimation (photons) Collimation - Primary collimators define maximum field size - Secondary collimators define actual field size in two transverse directions Beam s eye view: Target Primary collimator Filter Y Rotation of collimator assembly Monitor chambers X1 Y2 X2 Secondary collimators Y direction Secondary collimators X direction 0 X Y1 Beam Production, Characteristics and Shaping / / M. Sassowsky 61
62 Beam shaping: Collimation (electrons) Collimation - Primary collimators - Secondary collimators - Tertiary collimator (electron applicator) Scattered electrons used to saturate field edges Secondary collimator Without electron applicator Electron Applicator With electron applicator Beam Production, Characteristics and Shaping / / M. Sassowsky 62
63 Beam shaping: Blocks Block: device to adjust transverse field shape to target volume Mold for block is cut from styrofoam Block is made by casting Pb alloy (low melting point) in the mold Individually manufactured for each field => time consuming and labour intensive Beam s eye view: Cut A-A : Cut B-B : A A B B D D x x Beam Production, Characteristics and Shaping / / M. Sassowsky 63
64 Beam shaping: Multi Leaf Collimators (MLC) MLC: device to adjust transverse field shape to target volume Made from single small leafs Each leaf can be moved to its individual position under computer control Beam s eye view: Leaf shape: Leaf movement A Cut Beam Production, Characteristics and Shaping / / M. Sassowsky 64
65 Beam shaping: Multi Leaf Collimators (MLC) Beam Production, Characteristics and Shaping / / M. Sassowsky 65
66 Beam shaping: Wedges (1) Wedge: device or method to achieve a linear tilt of isodose curves in one transverse direction Wedge angle α: angle of isodose curve w.r.t. curve without wedge (at reference depth) α Beam Production, Characteristics and Shaping / / M. Sassowsky 66
67 Beam shaping: Wedges (2) Hard wedge: - Inserts in treatment head - Progressive decrease in intensity across the beam - Reduction of beam intensity => wedge transmission factor - Influence on beam quality Dynamic wedge: - Closing motion of one collimator jaw during irradiation - Modulation of dose rate Beam Production, Characteristics and Shaping / / M. Sassowsky 67
68 Beam shaping: Wedges (3) What are wedges used for? Application: 2 crossed fields Volume to be irradiated Beam Production, Characteristics and Shaping / / M. Sassowsky 68
69 Beam shaping: Wedges (4) Simple field setup: 2 crossed fields + = Inhomogeneous PTV coverage Beam Production, Characteristics and Shaping / / M. Sassowsky 69
70 Beam shaping: Wedges (5) Inhomogeneity due to depth dose distribution Beam 2 Transverse profile of beam 2 Sum Depth dose distribution of beam 1 Beam 1 Beam Production, Characteristics and Shaping / / M. Sassowsky 70
71 Beam shaping: Wedges (6) Inhomogeneity due to depth dose distribution Beam 2 Transverse profile of beam 2 (with wedge) Sum Depth dose distribution of beam 1 Beam 1 Beam Production, Characteristics and Shaping / / M. Sassowsky 71
72 Beam shaping: Wedges (7) Application: varying tissue thickness; e.g. treatment of breast cancer 2 tangential fields Without wedges With wedges 1 Overdosage Homogeneous PTV coverage 2 Beam Production, Characteristics and Shaping / / M. Sassowsky 72
73 Beam shaping: Dynamic beam delivery Beam shaping described so far: static i.e. beam shape dose not change while radiation is on (except dynamic wedge) => 3D conformal RT Dynamic beam shaping methods / special delivery techniques: - IMRT - Conformal Arc - Rapid Arc - VMAT - Spot scanning with protons - Tomotherapy - Will be described in dedicated talks later during this course Just as example: IMRT Beam Production, Characteristics and Shaping / / M. Sassowsky 73
74 Beam shaping: IMRT (1) IMRT: Intensity Modulated Radio Therapy Highly conformal dose application e.g. head & neck cancer PTV: 54 Gy Spinal cord: < 50 Gy Beam Production, Characteristics and Shaping / / M. Sassowsky 74
75 Beam shaping: IMRT (2) fields Beam Production, Characteristics and Shaping / / M. Sassowsky 75 4
76 Beam shaping: IMRT (3) 7 1 Each field is fluence modulated Beam Production, Characteristics and Shaping / / M. Sassowsky 76
77 Beam shaping: IMRT (4) Fluence modulation is achieved by moving the MLC while the beam is on Beam Production, Characteristics and Shaping / / M. Sassowsky 77
78 The end... Thank you for your attention! Questions? Beam Production, Characteristics and Shaping / / M. Sassowsky 78
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