SLAC KLYSTRON LECTURES

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• SLAC KLYSTRON LECTURES
• Lecture 14
• June 23, 2004
• 2-D and 3-D MAGIC Simulation Software
• Applied to Klystron Design Examples
• David Smithe and Larry Ludeking
• ATK Mission Research
• magic_at_mrcwdc.com
• George Caryotakis, Glenn Scheitrum, Daryl Sprehn,
  and Bob Steele
• Stanford Linear Accelerator Center

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Outline

• Example of Klystron Simulation in MAGIC Software
• Overview of FD-TD-PIC Computation Method
• Various Different Uses for the Software
• The B-Factory Klystron Template
• Challenges for the Future

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Geometry-Based Simulation Example 7 Cavity
Klystron
Voltage at Input Cavity
Voltage at Output Cavity
(Courtesy of SLAC)
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Klystron Output Cavity Example

• Penultimate and 5-stage output cavity.
• Beam is bunched in several previous cavities.
• (Magic 2D, simulation courtesy of SLAC.)

click for movie
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Theoretical Basis of MAGIC2D and MAGIC3D

• Maxwells Equations
• There are electromagnetic vector fields as a
  function of position, E(r), B(r), D(r), H(r), and
  particle current and charge fields, J(r), and
  r(r).
• Initial Conditions ??D r ??B 0
• Constitutive Relations E D / e H B / m
• Evolution Equations ?tB -??E ?tD ??H - J
• Relativistic Lorentz Force
• There are particles with position vector, xi, and
  relativistic momentum-per-mass vector, pi.
• Velocity Relation gi (1pi / c2)½ vi pi
  / gi
• Evolution Equations ?txi vi ?tpi (qi/mi)
  E(xi) vi ? Bi(xi)

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Theoretical Basis of MAGIC2D and MAGIC3D (cont.)

• Plus Many-Many Model Equations
• Materials (e, s, and m, perfect conductors,
  polarizers, foils, films, etc.)
• Boundary conditions (periodic, absorbing,
  transmission line, etc.)
• Particle Emission models (thermionic, secondary,
  explosive, etc.)
• Lumped circuit elements (resistor, inductor,
  cable, capacitor, etc.)
• Static magnetic fields (coils, imported from
  other codes, etc.)
• RF sources (voltage ports, current drivers,
  etc.)
• Initial conditions (field solver, particle
  populations, etc.)
• Feedback circuits

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Time Domain Simulation

• MAGIC is simulation, not analysis. The goal is
  to mimic nature, with as little a priori
  knowledge as possible. As with nature, one
  starts with an initial system state, and evolves
  the system forward in time, without prejudice as
  to what the future system will or should look
  like. Diagnostics allow the researcher to
  observe the system, and if fortunate, interpret
  what is happening in a physical sense.
• This is Time Domain. So MAGIC Is FD-TD-PIC.
• Simulation is essentially a metal-less
  laboratory.
• Example If a device must be properly tuned in a
  real laboratory, then it will need to be
  similarly tuned in simulation.
• Example If a device cant work in the
  laboratory, it will be very difficult, or
  hopefully impossible, to force it to work somehow
  in simulation.
• Example If the lab results are confusing, the
  simulation results might also be confusing. But,
  of course, MAGIC has diagnostics no lab has!

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Matrix Formulation

• Field components are E?dl, D?dA/dt,
• H?dl, and B?dA/dt.
• All derivatives, ?x , ??, and ?t, become
  matrices with 0,1.

Divergence of B Gausss Law Continuity
Faradays Law Amperes Law
Material Properties
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Uses for Simulation Software

• General qualitative understanding of physical
  processes
• Evaluation of difficult-to-predict parameters
  for spreadsheet analysis
• Plasma wave-number
• Trans-conductance
• Beam Loading, real and imaginary parts
• Evaluation of difficult-to-analyze components
• Penultimate and Output Cavities
• Magnetic focusing of time-dependent bunched-beam
• Entire end-to-end simulation

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Qualitative Understanding

• Many special diagnostics allow one to visualize
  the physics, and better understand it
• Example bunch behavior in an SBK output cavity
• It is usually simple to try unusual geometry or
  situations, once the basic geometry is in place
• Example one absent beam line in an MBK

click for movie
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Parameter Evaluation - Plasma Wavenumber

• Excite cavity, pass steady-state beam through it,
  and watch bunching develop as beam passes through
  long drift tube. Tells where to place next
  cavity.

¼ lp
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Parameter Evaluation Beam Loading

• Ring-down Simulation. Pump up cavity with beam
  present, turn off pump. Signal will decay,
  giving Qbeam. Oscillation will also shift
  frequency slightly to beam loaded frequency.

Beam Loaded Frequency
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Difficult Components Output Cavity

• In the output cavity
• Small-signal analysis is no longer valid
• Particles in bunches may overtake one-another
• Space charge forces are accentuated because of
  tight bunching
• Radial transport is significant
• Extended interaction regions imply more than one
  possible mode
• Coupler geometry may be significant
• Simulation is almost a necessity
• Example ¾ - p mode output cavity

click for movie
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Sheet Beam Output Cavity

• Uses 3-cavity extended interaction, coupler load
  in 3rd cavity end only
• Example Checking for constant phase across
  width of sheet beam

click for movie
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Difficult Components Acceleration of Bunched
Beam

• Klystron-like device, called a Reltron.
• Two stages of DC voltage applied
• Input cavity between the stages

click for movie
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Entire End-to-end Simulation of B-Factory Klystron
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The B-Factory Klystron Template

• Pre-written MAGIC2D input file of complete
  klystron, for public use
• Find it in Vacuum Electronics book by Barker et
  al.
• Find it at SLAC website
• User-friendly interface allows novices to
  redesign aspect of the klystron including cavity
  frequencies, Qs, spacings, and gap parameters.

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Template Design and Optimization Capability

• The template allows one to load previous results.
  The design iterative process is a repetition of
  device tuning runs, followed by a full-up
  hot-test run for result.

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Template Cavity Parameters

• Dialogs allow specification of all major cavity
  parameters

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Template Tuning Results

• Results of each iteration are tracked, and error
  between actual and desired values is given.

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Template Hot Test Setup

• Hot test parameters are set in a dialogue box

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Template Hot Test Run

• PHASESPACE plots during the hot test run show
  qualitative behavior

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Template Hot Test Results

• Results are provided in graphics and tabular form.

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Challenges for the Future Problem Size
Simulation Geometry

• Always need more cells in 3-D
• Example Multiple Beam Klystron
• Parallel processing will help.

Non-Uniform Grid
Grid resolution of Beam Tubes 12 cells across
tube.
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Challenges for the Future Relativistic Devices

• Numerical Cerenkov instability remains a
  manageable nuisance
• HIGH_Q algorithm damps instability without
  loading cavities
• Grid jiggling allows standard un-damped
  algorithms
• Still looking for more convenient solutions to
  the problem.

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Challenges for the Future Maintaining
Reliability

• SLAC has developed an HTML driven Automated Test
  Suite to allow fast verification of MAGIC results
  on a large suite of different test cases.
• Provides quick verification of new versions of
  the software.

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Summary

• The MAGIC software has been used for studying
  klystrons at SLAC for at least 8 years.
• As computer speed increases, the potential uses
  of the software have evolved from 2-D physics
  studies to 3-D design work.
• This talk has provided an overview and many
  examples of the use of the MAGIC software in
  klystron problems.
• An public klystron template, based on SLACs
  B-factory klystron is available for use,
  experimentation, and education.
• Parallel processing capability and active
  software development programs offer promise for
  even more capability in the future.