Design, Modeling and Simulations of a
Cabinet Safe System for a Linear
Particle Accelerator of intermediate
low energy by ...
Research foundations
Low energy accelerators systems (<1 MeV) have
established “cabinet safe” operation within several
met...
Research foundations
To accomplish the portability and safety operation of particle
accelerators in cargo inspection appli...
Research foundations
As a first step towards our final goal

Modeling, Simulation and Optimization
of the IAC-Varian Accel...
Research foundations
As a second step towards our final goal

Radiation studies of the standard and optimized models
of th...
Microwave Linacs Concepts

Klystron diagram

Transversal cut of a Clinac

Biperiodic SW structures: a) On
axis coupling an...
A short story about RF Cavities, Fields
and Beams

Pillbox Cavity

Structure Mode

Basic SW def.: 2pi
divided by number
of...
A short story about RF Cavities, Fields
and Beams
Equivalent circuit for a biperiodic
cavity chain. K1 represent the
magne...
A short story about RF Cavities, Fields
and Beams

Vector Z of particle optical
coordinates:

9/4/2008

Carlos O. Maidana
...
Electron emission
•Thermal electron emission (heated material)

•Field emission (high gradient field)
•Photo-cathode emiss...
Electron emission
Main Phenomena to take care of

• Multipacting

•Secondary Electron Emission

Back scattered secondary: ...
Focusing Solenoids approach
An important factor to take into consideration is the use of

focusing solenoids

Reduce the b...
Solenoid Focusing
We are familiar with 3 kinds of solenoid focusing:
1. Focusing in one or more larmor rotation in a
unifo...
Solenoid Focusing: canonical
momentum derivation
Starting from the relativistic Lagrangian the canonical
momentum of a par...
Solenoid Focusing: matrix formalism
The transfer matrix M of a solenoid
can be thought as the composition of
three differe...
Solenoid Fields
Bz ( s) 

B0
tanh(s / R)  tanh((s  l ) / R)
2 tanh(l / 2 R)

Thin solenoid - CMS: The hyperbolic tang...
ASTRA & COSY Infinity
ASTRA stands for A Space Charge Tracking Algorithm. The program ASTRA
tracks particles through user ...
Front End Solenoids
COSY Infinity result for 18 MeV electrons under
the influence of multiple B fields (FE solenoids +
Lin...
Waveguide Modeling of IAC-Varian
Accelerator Series
RF Cavities:
•Analytical determination of main RF accelerating field: ...
Waveguide Modeling of IAC-Varian
Accelerator Series
Confinement solenoids characteristics:
•Two long solenoids to confine ...
Waveguide Simulation of IAC-Varian
Accelerator Series
Final characteristics:
•871 macro particles reach the target positio...
Waveguide Simulation of IAC-Varian
Accelerator Series

Top, front and side view of the micro bunch. The
RMS Beam size is s...
Effect of Front End Solenoids on IACVarian Accelerator Series
Final characteristics:

•855 particles taken into account
•S...
Effect of Front End Solenoids on IACVarian Accelerator Series

The beam size and divergence are smaller and some
improveme...
Effect of Thin & Front End Solenoids on
IAC-Varian Accelerator Series
Final characteristics w/thin sol. @ 0.071 m:
•Micro ...
Effect of Thin & Front End Solenoids on
IAC-Varian Accelerator Series

9/4/2008

Carlos O. Maidana

26
Effect of a Multiple Solenoidal System
on IAC-Varian Accelerator Series

F.E. solenoids with same characteristics than bef...
Effect of a Multiple Solenoidal System
on IAC-Varian Accelerator Series
Final characteristics:
•Micro bunch charge: -1.99 ...
Effect of a Multiple Solenoidal System
on IAC-Varian Accelerator Series

Energy deposition due to particle
loss ~5.1 10-7 ...
Uncertainties due to Wakefields and
Accelerator Acceptance
The uncertainties in these models and simulations are given mai...
Gamma Shower results using Monte
Carlo methods for a generic Linac head.
Angular distribution of
electrons

Backscattered ...
Electron Gun Characterization
One of the most used electron guns in microwave
accelerators

Pierce electron gun
Schematic ...
Electron Gun Characterization

9/4/2008

Carlos O. Maidana

33
Electron Gun Characterization
Beams in general

Non uniform density profile

When the beam currents are high enough that s...
Electron Gun Characterization

•A way to optimize the injection of electrons emitted from the gun is the
placing of a thin...
Electron Gun Characterization

Time resolved images of a low current electron beam generated in a Pierce gun after transpo...
Electron Gun Modification
Specifications for a new e-gun
Pulses of ~200 s length and ~ 5nC charge
Bunches of ~1 ns (macro...
Electron Gun Modification

Effect of adjusting the control grid bias in a triode electron gun for optimal beam output. The...
Estimation of photons and dose
transmitted by the RF cavities.

Photons transmitted by the main
radiated cavities in the I...
Estimation of improvements using
the Multiple Solenoidal System.
Maximum estimated dose
transmitted by the cavities

0.005...
Conclusion
Electron gun modification
Optimization
Multiple Solenoid System

Reduction of Radiation Emitted
is expected

Ba...
Acknowledgement
Dr. Alan W. Hunt (IAC-ISU)
Dr. Klaus Floettmann (DESY)
Dr. Shashikant Manikonda (ANL)

Dr. Alberto Rodrigu...
T4 6 MeV Accelerator

Agreement with the
measurements done by
D. Wells and F. Harmon
in the IAC’s T4.

Last/exit cavity

9...
Emittance and Liouville’s theorem
Liouville's theorem tells us that under symplectic transport, particle densities in
phas...
GDR Neutron yield and differential
photon track length distributions
Total photoneutron yield
cross sections for W & Cu.

...
Neutron Sources in IAC-Varian
waveguides

9/4/2008

Carlos O. Maidana

46
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Maidana - Modification of particle accelerators for cargo inspection applications

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As part of an accelerator based Cargo Inspection System, studies were made to develop a Cabinet Safe System by Optimization of the Beam Optics of Microwave Linear Accelerators of the IAC-Varian series working on the S-band and standing wave pi/2 mode. Measurements, modeling and simulations of the main subsystems were done and a Multiple Solenoidal System was designed.
This Cabinet Safe System based on a Multiple Solenoidal System minimizes the radiation field generated by the low efficiency of the microwave accelerators by optimizing the RF waveguide system and by also trapping secondaries generated in the accelerator head. These secondaries are generated mainly due to instabilities in the exit window region and particles backscattered from the target. The electron gun was also studied and software for its right mechanical design and for its optimization was developed as well. Besides the standard design method, an optimization of the injection process is accomplished by slightly modifying the gun configuration and by placing a solenoid on the waist position while avoiding threading the cathode with the magnetic flux generated.
The Multiple Solenoidal System and the electron gun optimization are the backbone of a Cabinet Safe System that could be applied not only to the 25 MeV IAC-Varian microwave accelerators but, by extension, to machines of different manufacturers as well. Thus, they constitute the main topic of this paper.

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Maidana - Modification of particle accelerators for cargo inspection applications

  1. 1. Design, Modeling and Simulations of a Cabinet Safe System for a Linear Particle Accelerator of intermediate low energy by optimization of the beam optics. Carlos O. Maidana, Ph.D.* *Currently at Washington State University and Idaho National Laboratory
  2. 2. Research foundations Low energy accelerators systems (<1 MeV) have established “cabinet safe” operation within several meters of the accelerator. Higher energy systems (1 – 25 MeV) needs the same convenience and portability as low energy systems For its use in cargo inspection applications Which requires transportation and operation in harbors and borders. 9/4/2008 Carlos O. Maidana 2
  3. 3. Research foundations To accomplish the portability and safety operation of particle accelerators in cargo inspection applications Beam Dynamics needs to be optimized and shielding minimized Meaning reduction of the radiation field must be done by other means such as Beam Optics. 9/4/2008 Carlos O. Maidana 3
  4. 4. Research foundations As a first step towards our final goal Modeling, Simulation and Optimization of the IAC-Varian Accelerators had to be done. 9/4/2008 Carlos O. Maidana 4
  5. 5. Research foundations As a second step towards our final goal Radiation studies of the standard and optimized models of the IAC-Varian Accelerators had to be done as well. 9/4/2008 Carlos O. Maidana 5
  6. 6. Microwave Linacs Concepts Klystron diagram Transversal cut of a Clinac Biperiodic SW structures: a) On axis coupling and b) side-cavity coupling. --------------->>>>>>> Standing Wave oscillating in amplitude vs. time. 9/4/2008 Carlos O. Maidana Source: Karzmark, Nunan, Tanabe; Medical Electron Accelerators, McGraw Hill. 6
  7. 7. A short story about RF Cavities, Fields and Beams Pillbox Cavity Structure Mode Basic SW def.: 2pi divided by number of cavities per wavelength. 9/4/2008 Cavity Mode TE: Transversal Electric TM: Transversal Magnetic Carlos O. Maidana 7
  8. 8. A short story about RF Cavities, Fields and Beams Equivalent circuit for a biperiodic cavity chain. K1 represent the magnetic coupling constant between on-axis and off-axis cavities; K2 represents the one between adjacent accelerating cavities and K3 between adjacent o ff - axi s ca v iti e s . Dispersion relation The accelerating cavities resonant frequency is w1 and the coupling cavity one is w2. Always assuming n=0,2,…,2N accelerating cavities and n=1,3,…,2N-1 coupling cavities. f is the mode number, which is given by f=pq/(2N) with q=0,1,…,2N. Typical values are k1=0.03, k2=-0.002 and k3=0. 9/4/2008 Carlos O. Maidana 8
  9. 9. A short story about RF Cavities, Fields and Beams Vector Z of particle optical coordinates: 9/4/2008 Carlos O. Maidana Source: Wilson and Wolski academic lectures. 9
  10. 10. Electron emission •Thermal electron emission (heated material) •Field emission (high gradient field) •Photo-cathode emission (photoelectric effect) •Secondary electron emission (induced by electron absorption) Fermi-Dirac distribution. T=0, Fermi level. T>0, Higher Energy state due to thermal energy. 9/4/2008 Thermal emission: If T is high enough the e are distributed up to the vacuum level and e can scape Carlos O. Maidana Field emission: with a larger surface field, the potential barrier to the outside becomes thinner. When E>1E8 V/m the tunnel current becomes important. 10
  11. 11. Electron emission Main Phenomena to take care of • Multipacting •Secondary Electron Emission Back scattered secondary: when the primary electron is reflected off the surface Resonance multiplication of secondary electrons Rediffused secondary: the electron penetrates the surface and scatters off one or more atoms and is reflected back out One electron impact with a surface releasing more secondary electrons True secondary electrons: the electron interacts inelastically with the material and releases more electrons 9/4/2008 Carlos O. Maidana 11
  12. 12. Focusing Solenoids approach An important factor to take into consideration is the use of focusing solenoids Reduce the beam envelope Reduce the beam divergence and so the possibilities of secondary emission and/or highly dispersive radiation effects. 9/4/2008 Carlos O. Maidana 12
  13. 13. Solenoid Focusing We are familiar with 3 kinds of solenoid focusing: 1. Focusing in one or more larmor rotation in a uniform long solenoid (as in an image intensifier). 2. The trapping of articles along field lines. 3. Focusing from point to point by a thin solenoid. 9/4/2008 Carlos O. Maidana 13
  14. 14. Solenoid Focusing: canonical momentum derivation Starting from the relativistic Lagrangian the canonical momentum of a particle of charge q can be expressed as:   L    P    m0v  qA  p  qA  qi If E=0 in the region where the solenoid is placed, then the canonical momentum is conserved due to the position independence of the Hamiltonian. If a particle goes from a region of magnetic field to a region with zero magnetic field, it experiments a change in momentum 1 pf  qAf  qrB0 ( z ) 2 The particles crossing the fringe fields experience a transverse force (kick in the azimuthal momentum) causing the particles to follow a spiral path & a coupling between coordinates. 9/4/2008 Carlos O. Maidana 14
  15. 15. Solenoid Focusing: matrix formalism The transfer matrix M of a solenoid can be thought as the composition of three different matrices corresponding to : •M1: entrance fringe field, •M2: constant axial magnetic field & •M3: output fringe field. M linear 9/4/2008 0 0 1 0 0 1 0  1/ f 0 0 0 qB 2p 1 0 0 1 0  0 0  1  0  0  0  1   1   0 M3    0  qB  2p    1  0 M2     0    sin f  p sin f qB cos f p  (1  cos f ) qB 0  C    CS M    CS  S 2  CS /  C2  S 2 /  CS 2 f-1=[(qB)/(2p)]2L  1    1/ f  0   0   1   0 M1    0  qB  2p  Carlos O. Maidana CS  S 2 C2  CS Taylor 1st order 0 0 qB 1  2p 0 1 0 0 0  0  0  1  p  (1  cos f )  qB  sin f   p sin f  qB   cos f  0 0 1 0 S /   CS  CS /    C2   2 w h e r e S=sin(q/2), C=cos(q / 2 ) , a=qB/2p and q =2La if L is the total length of the solenoid. 15
  16. 16. Solenoid Fields Bz ( s)  B0 tanh(s / R)  tanh((s  l ) / R) 2 tanh(l / 2 R) Thin solenoid - CMS: The hyperbolic tangents are used as simple approximations for the rise and fall-off of the field at s=0 and s=l. •The tanh approximation is used because the on-axis field drops more quickly in the fringe region compared to the pure theoretical fields. But, the discrepancy from the actual field becomes large for sufficiently thick solenoids. 0 In     Bz ( s)   2 2  2  s2  R2 (s  l )  R   s s l  R  R2  s2 0 In  2  s log 2 Bz ( s)   R  R2  s2 2( R2  R1 )  1  1  9/4/2008 Thin Solenoid – CMSI: this element is a thin solenoid made of a single layer of thin wire 2 2     ( s  l ) log R2  R2  ( s  l )   R  R 2  (s  l )2 1   1 Carlos O. Maidana     Thick Solenoid – CMST : this element is a thick solenoid extending longitudinally & radially 16
  17. 17. ASTRA & COSY Infinity ASTRA stands for A Space Charge Tracking Algorithm. The program ASTRA tracks particles through user defined external fields taking into account the space charge field of the particle cloud. The tracking is based on Runge-Kutta integration of 4th order with fixed time step. ASTRA was developed in DESY Hamburg by Dr. Klaus Floettmann. COSY Infinity is a code for the study and design of beam physics systems. At its core it is using Differential Algebraic (DA) methods and it allows the calculation of arbitrary order effects of particle optical elements. COSY Infinity is an object oriented language environment. COSY was developed in Michigan State University by Dr. Martin Berz et al. 9/4/2008 Carlos O. Maidana 17
  18. 18. Front End Solenoids COSY Infinity result for 18 MeV electrons under the influence of multiple B fields (FE solenoids + Linac’s thick solenoid). •The particle was launched inside the Linac solenoidal field. •Each beam was set up to: 6 mm in size and 200mRad aperture. •Symmetry between the x-a(=px/p0) and y-b(=py/p0) planes can be observed Bz field at the center of the solenoids: +/- 0.745 T Drift Length: 0.1147 m Drift between first solenoid and Linac: 0.05 m The objective of the fitting algorithm was to minimize (x,a), ( y, b ) a n d t o k e e p s t a b i l i t y. Aperture (radius): 0.1015 m It’s clear that beam focusing and trapping of particles can be accomplished by the used of thin solenoids. 9/4/2008 Carlos O. Maidana 18
  19. 19. Waveguide Modeling of IAC-Varian Accelerator Series RF Cavities: •Analytical determination of main RF accelerating field: TM010 •Metrology of apertures using image processing software •Generation of data files Solenoids: •Mapping of axial magnetic fields generated by the Linac integrated solenoids •Generation of data files Beam: •Distribution characterization: Plateau for the bunch, Gaussian for the micro-bunch •Efficiency from injection to exit •Characterization of the beam emitted from the gun Source: SLAC-PUB-8026 9/4/2008 Carlos O. Maidana 19
  20. 20. Waveguide Modeling of IAC-Varian Accelerator Series Confinement solenoids characteristics: •Two long solenoids to confine the electrons to the waveguide and to avoid multipacting •External diameter: 25.5 cm; inner diameter: 21.5 cm. •Length: 1.04 m and 0.33 m •Operating points: 15.7 A at 137 V (long sol.) and 15.5 A at 42 V (short sol.) Initial beam characteristics: •8000 macro particles taken into account •Gaussian distribution with sx,y=0.75 mm •Quasi-randomly distribution using the Hammersley sequence to reduce statistical fluctuations and to avoid artificial correlations •Micro-bunch charge: -2nC ; Energy: 50 KeV 9/4/2008 Carlos O. Maidana 20
  21. 21. Waveguide Simulation of IAC-Varian Accelerator Series Final characteristics: •871 macro particles reach the target position •Secondaries: ~0.021% of the injected charge •Beam size sx,y~1.1 mm •Micro-bunch charge: 0.2178nC (10.89%) •Energy: ~18 MeV (~14 MeV due to TM010) •Active secondaries: 0.0025% of injected charge. Longitudinal particle position showing the interaction point of the electrons within the waveguide and with the target. The stars at ~1.6 m represent the normal macro-particles reaching the target; the dark circles represent lost macro-particles and the gray ones are macro-particles traveling backwards. Secondaries generated at the exit window are not shown. 9/4/2008 Cavity 0 1 2 3 22 Energy [MeV] 0.50 1.30 2.1 2.9 18 Charge lost [%] 56 22.5 10 2 < 0.1 Carlos O. Maidana 21
  22. 22. Waveguide Simulation of IAC-Varian Accelerator Series Top, front and side view of the micro bunch. The RMS Beam size is sx, y ~ 1.1 mm.  E p    max  Ep E p ,max  s  Ep s 1  E  p ,max     s Secondary electrons emission yield, defined as the ratio of the number of emitted electrons to the number of incident electrons to the solid. Beam size evolution through the waveguide. 9/4/2008 Carlos O. Maidana 22
  23. 23. Effect of Front End Solenoids on IACVarian Accelerator Series Final characteristics: •855 particles taken into account •Secondaries: ~0.021% of the injected charge •Micro bunch charge: -0.2138nC •Beam size sx,y~0.63 mm •Average energy: ~14 MeV •Particle lost: ~90% 9/4/2008 Carlos O. Maidana 23
  24. 24. Effect of Front End Solenoids on IACVarian Accelerator Series The beam size and divergence are smaller and some improvements can be seen at the exit of the Linac, b u t n o t i m p o r t a n t o p t i mi z a t i o n s c a n b e accomplished by the used of only FE solenoids besides stronger focusing and trapping of secondary particles generated in the exit port. Very few improvements from the beam dynamics and linac performance point of view respecting the original model. 9/4/2008 Carlos O. Maidana 24
  25. 25. Effect of Thin & Front End Solenoids on IAC-Varian Accelerator Series Final characteristics w/thin sol. @ 0.071 m: •Micro bunch charge: -0.3965 nC (20%) •Beam size sx,y~2.4 mm •Average energy: ~14 MeV •Active secondary electrons: 2% total particles •Particle lost: 80% of the injected one Longitudinal particle distribution (interaction points with matter) for IAC-Varian Accelerator coupled to FE solenoids and a thin 0.087 T solenoid over the first full cavity. The circles close to the horizontal axis represents some few particles lost traveling backwards. 9/4/2008 Carlos O. Maidana 25
  26. 26. Effect of Thin & Front End Solenoids on IAC-Varian Accelerator Series 9/4/2008 Carlos O. Maidana 26
  27. 27. Effect of a Multiple Solenoidal System on IAC-Varian Accelerator Series F.E. solenoids with same characteristics than before Thin solenoids located at: 0.0005(0); 0.071(1); 0.228(4); 0.65(12) m (cavity) Thin sol. characteristics: 0.08718 T on axis 0.025 m length; 0.14 m radius 9/4/2008 Carlos O. Maidana 27
  28. 28. Effect of a Multiple Solenoidal System on IAC-Varian Accelerator Series Final characteristics: •Micro bunch charge: -1.99 nC (99%) •Beam size sx,y~1.9 mm •Average energy: 18 MeV (14.2 MeV TM010) •Active secondary electrons: 0 •Macro particle loss: 0.1% Longitudinal particle positions (interaction points) for the Multiple Solenoidal System. Very few macro-particles lost at the beginning of the waveguide (cavity 0) and more than 89% (±10%) of the injected ones reaching the final tracking position at z=1.60 m. The secondaries generated, and the particles lost, on the exit port/window are not considered here and represent a source of uncertainties to take into consideration. 9/4/2008 Carlos O. Maidana 28
  29. 29. Effect of a Multiple Solenoidal System on IAC-Varian Accelerator Series Energy deposition due to particle loss ~5.1 10-7 J/m Huge improvements could be accomplished by the used of a Multiple Solenoidal System 9/4/2008 Carlos O. Maidana 29
  30. 30. Uncertainties due to Wakefields and Accelerator Acceptance The uncertainties in these models and simulations are given mainly by: •Model and simulation of the bunching system is difficult without precise phase information. •Maximum acceptance for a bunching system is ~80% (being this last only accomplished in RFQ systems). •Wakefields modify the way that a cavity interacts with the beam and its calculations are still a topic of research. •Dipole mode could have some influence but it would be limited for this particular type of accelerator. As we know, dipole modes are transverse fields deflecting the particles if it is strong enough but it is my belief that the beam loading will avoid reaching the point of instabilities (i.e. TM110 generates dipole modes). 9/4/2008 Carlos O. Maidana 30
  31. 31. Gamma Shower results using Monte Carlo methods for a generic Linac head. Angular distribution of electrons Backscattered primary electrons: 0.346% Angular distribution of photons 9/4/2008 Carlos O. Maidana 31
  32. 32. Electron Gun Characterization One of the most used electron guns in microwave accelerators Pierce electron gun Schematic of a thermo ionic e-source. Electrons have a Boltzmann distribution of energies. Based on the Rodney-Vaughan method an algorithm for the complete characterization of the gun was developed using the VBasic language. 9/4/2008 Figure. Converging gun geometry for a beam with moderate perveance. Courtesy Field Precision LLC. Carlos O. Maidana 32
  33. 33. Electron Gun Characterization 9/4/2008 Carlos O. Maidana 33
  34. 34. Electron Gun Characterization Beams in general Non uniform density profile When the beam currents are high enough that self fields (space charge effects) can no longer be neglected in comparison to the applied fields, then the analysis becomes more difficult and complex. Beam profile for electrons created in a Pierce gun with 25 mA current at 10 keV voltage. It is clear that they don’t follow a Gaussian distribution because of the presence of strong space charge forces in their center. Picture created by Matt Hodek (MSU) with experimental data taken with Carlos O. Maidana (WSU) and Adam Lichtl (BNL) on a diode Pierce gun at the University of Maryland, College Park. 9/4/2008 Carlos O. Maidana 34
  35. 35. Electron Gun Characterization •A way to optimize the injection of electrons emitted from the gun is the placing of a thin solenoid on the waist position. •Calculation of the solenoid parameters is done using COSY Infinity. The objective imposed is stability of the transfer map and the corresponding conditions for focusing or parallel movement. 9/4/2008 Carlos O. Maidana 35
  36. 36. Electron Gun Characterization Time resolved images of a low current electron beam generated in a Pierce gun after transport through a thin focusing solenoid. A higher density of electrons can be appreciated in the front center of the beam while a higher electron density distribution is located at the edges in the middle of the beam pulse. Images taken by Tiago Da Silva (University of Sao Paulo) and Carlos O. Maidana (WSU) at the University of Maryland, College Park. 9/4/2008 Carlos O. Maidana 36
  37. 37. Electron Gun Modification Specifications for a new e-gun Pulses of ~200 s length and ~ 5nC charge Bunches of ~1 ns (macro-inner pulse) Bunch separation of ~1 s Micro-bunch structure: S band (2.586 GHz) 9/4/2008 Carlos O. Maidana 37
  38. 38. Electron Gun Modification Effect of adjusting the control grid bias in a triode electron gun for optimal beam output. The disadvantage for high currents is the higher erosion rate that such a grid can suffer. Courtesy of Dr. Santiago Bernal, UMER – University of Maryland, College Park. 9/4/2008 Carlos O. Maidana 38
  39. 39. Estimation of photons and dose transmitted by the RF cavities. Photons transmitted by the main radiated cavities in the IAC-Varian Linacs Dose rate transmitted by the main radiated cavities in the IAC-Varian Linacs (water phantom: 94.01 rads/h; empty phantom: 115.57 rads/h). 9/4/2008 Carlos O. Maidana 39
  40. 40. Estimation of improvements using the Multiple Solenoidal System. Maximum estimated dose transmitted by the cavities 0.005 rads/h Minimum estimated dose transmitted by the cavities 0.001 rads/h 9/4/2008 Carlos O. Maidana 40
  41. 41. Conclusion Electron gun modification Optimization Multiple Solenoid System Reduction of Radiation Emitted is expected Basis for a Cabinet Safe System Development Method 9/4/2008 Carlos O. Maidana 41
  42. 42. Acknowledgement Dr. Alan W. Hunt (IAC-ISU) Dr. Klaus Floettmann (DESY) Dr. Shashikant Manikonda (ANL) Dr. Alberto Rodriguez (CERN) Mr. Mike Smith (IAC-ISU) This research is being developed thanks to the U.S. Department of Defense. 9/4/2008 Carlos O. Maidana 42
  43. 43. T4 6 MeV Accelerator Agreement with the measurements done by D. Wells and F. Harmon in the IAC’s T4. Last/exit cavity 9/4/2008 Carlos O. Maidana 43
  44. 44. Emittance and Liouville’s theorem Liouville's theorem tells us that under symplectic transport, particle densities in phase space must be conserved. The symplectic condition for Liouville's theorem to be satisfied is that the dynamics of individual particles must be governed by Hamilton's equations. This is the case for particles moving along an accelerator beam line if: – we neglect dissipative effects like radiation; – we keep a constant reference momentum, P0. Assuming that Liouville's theorem holds, the emittance of a bunch must be conserved as the bunch moves along an accelerator beam line. 9/4/2008 Carlos O. Maidana 44
  45. 45. GDR Neutron yield and differential photon track length distributions Total photoneutron yield cross sections for W & Cu. Differential photon track length distributions produced in 1-radiation length-thick W targets struck by 10, 15 and 20 MeV electrons Source: Mao, Kase, Liu and Nelson, Neutron sources in the Varian Clinac 2100C/2300C Medical Accelerator Calculated by the EGS4 Code, SLACPUB-7077, June 1996. 9/4/2008 Carlos O. Maidana 45
  46. 46. Neutron Sources in IAC-Varian waveguides 9/4/2008 Carlos O. Maidana 46

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