A Tutorial on Nonintercepting Electromagnetic Monitors for Charged Particle Beams Bob Webber January

1
A Tutorial on Non-intercepting Electromagnetic
Monitors for Charged Particle Beams Bob
WebberJanuary 30, 2008

• AD Beam Instrumentation

2
Electromagnetic Monitors for Charged Particle
Beams

• Electromagnetic beam monitors offer a
  non-disruptive means to observe and quantify
  properties of the beam itself or, with the beam
  as a probe, of the accelerator or transport line
  in which the beam travels
• Fundamental parameters that can be measured
  include
• beam current
• temporal distribution of particles
• transverse position of the beam in the chamber
• Monitors are designed to sample the beams
  electric field, magnetic field, or a combination
  of each
• Monitors that interact primarily with the
  electric field are typically called electric or
  capacitive monitors
• Monitors that interact primarily with the
  magnetic field are typically called magnetic
  monitors or current transformers

3
Signals and Sensitivities

• A capacitive pickup signal
• Polarity depends on the sign of the beam
  particles charge
• Amplitude is independent of the direction the
  beam is traveling
• A magnetic pickup signal
• Polarity determined by the product of particle
  charge and direction of travel, i.e. the sign of
  electric current
• Amplitude is independent of the direction the
  beam is traveling
• An electromagnetic pickup signal coupled to
  both the electric and magnetic fields
• Polarity depends on the relative electric and
  magnetic coupling
• Amplitude response can depend on the direction of
  beam travel without regard to the particle charge
  like a directional power coupler

4
A Model Charge Distribution
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Beam Current of Distribution
To an observer at a fixed position in x, the
distribution presents a bunch frequency of
f  ßc/Lb. The beam current of this charge
distribution, observed at x 0 is
where ? 2?f. The zero-frequency term of
magnitude ßcA is the DC or average beam
current. This simple single-frequency model
presents no loss of generality, since any real
charge distribution can be described by a Fourier
series, a linear superposition of terms with
different frequencies and phases.
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The Beam as a Signal Source

• The beam appears as nearly an ideal current
  source, that is, the beam current is unaffected
  by interaction with the monitor.
• The source impedance, the change in terminal
  voltage required to effect a change in current,
  is described as
• For 10 mA, 10 MeV beam, find 4E11 ohms for
  electrons, 2E9 ohms for protons!
• Significant exceptions like beam instabilities
  are possible when the beam interacts repeatedly
  with a periodic structure.

• V i R i Z

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The Beam Environment

• The beam and its environment communicate
  through the electric and magnetic fields
• Typically the beam travels through an evacuated
  chamber bounded by an electrically conducting
  metallic wall
• The beam, an assembly of charged particles,
  carries an electric field which induces image
  charge on the chamber wall
• The beam, as charged particles in motion,
  carries a magnetic field that, at sufficiently
  high frequency, induces the image charge to flow
  with it. The resulting wall currents are, to
  first order, equal and opposite to the beam
  current

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An Artists Conception of the Fields
Electric
Q
Q
Velocity ß ? 1
Isolated charge at rest
Charge at rest in pipe
Charge at relativistic velocity
Magnetic Beam into page
At moderate and high frequency, no field outside
chamber
At DC, fields penetrate chamber
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Beam E/M Field Attenuation

• To the extent that wall currents mirror the
  beam current, the magnetic field outside the beam
  tube is cancelled
• This field strength reduction corresponds to
  the attenuation of electromagnetic waves
  propagating through a conductor
• The characteristic length in which the fields
  are reduced by a factor of e (-8.69 dB) is
  termed the skin depth
• The skin depth in a non-magnetic good conductor
  is
• where ? is the resistivity of the conductor in
  ohm-meter and f is the frequency of interest in
  Hz

10
Energy Flows through the Dielectric

• Chart of skin depth in millimeters
• A 1/32 stainless beam tube wall is 6.1 skin
  depths at 10Mhz and attenuates magnetic fields
  propagating to the exterior by 53dB
• Not so much as to make the beam signal invisible
  to a sensitive radio receiver
• Sufficient to clobber the sensitivity of a
  practical beam current monitor
• Hence beam monitors generally must be placed
  inside the beam chamber

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A Typical Messy Environment
Lines of induction around isolated circulating
beam
Wall current induced in beam tube attenuate
external field
Break in tube impedes wall current
Typical complex and distributed paths available
to induced currents
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A Capacitive (Electric Field) Pickup
An isolated cylindrical electrode with length Le
and radius a inside tube with radius b. Electric
field lines from beam can terminate on electrode,
but no loop area is present to intercept magnetic
flux.
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Estimating the Signal

• Assuming a purely transverse electric field,
  the charge induced on the inside of the
  capacitive electrode at any time is equal to the
  total beam charge contained within the linear
  extent of the electrode and opposite in sign.

Solving the integral gives
The first zero in this sin(x)/x frequency
response shape occurs where Le Lb

• Wrong High Frequency Limit

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When Propagation Time Matters

• Missing is consideration of the time delay for
  a charge induced at any position along the
  electrode to be recognized at the tap point. This
  information can only travel at the speed of an
  electromagnetic wave, the speed of light, for a
  monitor with vacuum as the only dielectric. At
  low frequencies the effect is negligible where
  transit times are a significant fraction of the
  period and the bunch length is comparable to the
  electrode length, the impact is large.
• Accounting properly for signal propagation
  times (ignoring azimuthal effects on the
  assumption of cylindrical symmetry including beam
  position), the effective charge observed at the
  tap point at any time is the sum of the charges
  induced at all longitudinal segments of the
  electrode at a time earlier by an amount x/v,
  where x is the position of the segment relative
  to the tap point and v ßc for vacuum.

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Mathematically

• Mathematically the time at each position along
  the electrode is weighted by the transit time to
  the tap point. The expression for the induced
  charge as observed at the tap point becomes
• And the available signal current is

• Correct High Frequency Limit !

The first zero occurs where Le Lb/2
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Signal Power from Capacitive Pickup

• In the short electrode limit, LeltltLb, the tap
  point current is

In the frequency domain, the signal voltage on
load resistor R becomes
where Z is parallel combination of R and
Celectrode and t R Celectrode
Signal power for ? gtgt 1/t is
V2/R (1/R)(ALe/C) 2 (ALe) 2/(Ct)
with capacitance
The resulting signal power for ? gtgt 1/t is
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A Window to the Beam

• Since the magnetic field of the beam is
  severely attenuated outside a continuous
  conducting vacuum chamber, a practical beam
  current monitor must either be placed within the
  vacuum chamber walls or the conducting path in
  the chamber must be broken
• To minimize the mechanical complications of
  inserting a device into the vacuum, a
  non-conducting material, often ceramic, is
  typically inserted in a section of the beam tube
• This break in the beam tube conduction path
  forces wall currents to find a new path,
  potentially under the instrument designers
  control, outside the vacuum chamber

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The Ceramic Break
Typical Ceramic Break Installation
Circuit Model

• Beam tube capacitance, grounds, and ungrounded
  parallel connections may be intentional or
  incidental, local or distant, but something will
  always be present
• Zgap is combination of the gap capacitance and
  all external parallel elements
• Gap voltage
  will be generated

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Location of Current Monitor Relative to Gap

• OK - only beam currents, not wall currents will
  pass through monitor
• NOT OK - wall currents bypass gap through grounds
  then proceed through monitor

OK - wall currents cannot bypass gap to flow
through monitor NOT OK - wall currents
bypass gap through grounds then proceed through
monitor
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Impedance Measured Across Ceramic Gap on Beam
Tube Courtesy of Jim Crisp/Mike Reid
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Controlling the Environment and Taming the Gap
Impedance

• Zshunt is applied to control potentially high
  gap impedances
• Strap or housing around the transformer and gap
• Short circuits external currents that might flow
  through Zshunt and produce undesired monitor
  signals
• Shields external world from the beam current and
  gap voltage

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The Beam Current Transformer Model
Magnetic flux due to any winding k
Total flux is sum of that due to all currents,
beam and signal
Beam acts as single-turn primary winding
Voltage on any winding
Signal power at mid-band frequencies
Frequency response
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Compare Signal Power from Capacitive and Magnetic
Pickups of Same Time Constant
Above low frequency corner

• In the absence of magnetic or dielectric
  materials, µr er 1, the power from the
  magnetic monitor can never exceed that from the
  capacitive monitor.
• For non-relativistic beams, the capacitive
  monitor provides greater signal power than the
  magnetic monitor by a factor of 1/ ß2.
• For relativistic beams the available power from
  the two monitors is identical.
• The addition of magnetic or dielectric
  material enhances the relative performance of the
  magnetic monitor, an advantage that can be
  dramatic as commonly available magnetic materials
  can offer permeability gt 10,000. Hence, the
  predominance of magnetic type beam current
  monitors.
• Capacitive monitors, in the relativistic beam
  regime, can offer benefits in instances where the
  signal power is adequate and at high frequencies
  where the advantage of magnetic materials can be
  lost.

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Magnetic Loop Pickup
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Directional Coupler
Equal signal out and along line
Zo
Zo
Zo
Zo
No signals
2Le
Zo
Zo
Zo
Zo
Forward line signal and opposite prompt signal
cancel at downstream port and opposite polarity
signal propagates backwards along line
Resulting signal at upstream port
Upstream port signal also zero in steady state
case if electrode electrical length is ½ bunch
spacing !
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Conclusion

• A conceptual introduction to electromagnetic
  beam monitors was presented from basic principles
• Models for estimating signal strength from both
  capacitive and magnetic monitors were shown and
  the relative signal strength from the two types
  was given
• A model for understanding a directional coupler
  monitor was outlined
• Hopefully the talk stimulates each listener to
  develop his/her own understanding of these basic
  processes in addition to the formal mathematics
  and to ask how does it work at a fundamental
  level

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Previous Tutorials

• First Workshop, 1989, BNL, Upton, NY ---
  Accelerator Instrumentation, AIP Conference
  Proceedings 212, New York American Institute of
  Physics, 1990.
• Longitudinal Emittance An Introduction to the
  Concept and Survey of Measurement Techniques
  Including Design of a Wall Current Monitor, pp.
  85-125.
• Sixth Workshop, 1994, Vancouver, BC, Canada ---
  Beam Instrumentation Workshop, AIP Conference
  Proceedings 333, New York American Institute of
  Physics, 1995.
• Charged Particle Beam Current Monitoring
  Tutorial, pp. 3-23.
• Ninth Workshop, 2000, Cambridge, MA --- Beam
  Instrumentation Workshop 2000, AIP Conference
  Proceedings 546, New York American Institute of
  Physics, 2000.
• Tutorial on Beam Current Monitoring, pp.
  83-104.

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Backups
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Toroidal Flux and Inductance
Lines of magnetic induction, B, encircle a
current i. In a homogeneous region near the
current, B is a function of radius from the
current is given by Amperes Law. constant at any
i is wihre B is constant and any radius and the
path of intergration is a circule around the wire
and has magnitude 2pir. Assume toroid of inner
radius a, outer radius b, and height (thickness) h
Assume toroid of inner radius a, outer radius b,
and height (thickness) h
Total flux is sum of that due to all currents,
beam and signal
Single-turn winding with current i
Voltage on any winding
Signal power at mid-band frequencies
Frequency response
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Common Types of Beam Current Transformers

• Integrating Current Transformer (ICT)
• Passive current transformer depending on short (lt
  1 nsec), isolated (50 nsec) beam bunch to drive
  impulse response of transformer
• Output pulse shape is fixed by design and
  independent of shape of sufficiently short beam
  pulse
• Output amplitude is directly proportional to
  charge of beam pulse
• Useful in synchrotrons, storage rings, and
  transport lines provided short isolated bunch
  criteria are met
• Advantage
• Simple, relatively inexpensive, stable passive
  calibration
• Output stretched in time relative to very short
  beam pulse
• Disadvantage
• Bunch shape information is not available

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Common Types of Beam Current Transformers

• Direct Current Transformer (DCCT, PCT, etc.)
• A strong well-controlled magnetizing force is
  applied to one or more toroids enabling sampling
  of magnetic bias imposed by beam
• Operates in zero flux mode, a feedback current
  equal and opposite to the beam is driven through
  the toroidal cores of the device
• Practical DCCTs for particle beams are a
  combination DC section and AC transformer to
  prevent aliasing and extend bandwidth
• Useful in synchrotrons and storage rings, not
  transport lines
• Advantages
• Measures 0 Hz (DC) component of bunched or
  unbunched beams
• Long term stability and lt1 microampere DC
  resolution
• Disadvantage
• Relatively expensive for applications not
  requiring DC response

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Common Types of Beam Current Transformers

• Classical AC Transformer
• Beam current couples magnetic flux to toroidal
  transformer core inducing current in sense
  winding on same core
• Output signal can provide hi fidelity
  representation of beam current pulse shape over
  wide bandwidth (10s of Hz to few MHz)
• Passive device that can be supplemented with
  various active circuits to modify performance
  (e.g. Hereward and active-passive
  configurations
• Advantages
• Simple and available in many configurations to
  suit application
• Disadvantages
• NOT DC coupled, provides NO DC output component

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Zshunt

• Circuit elements as depicted are often used to
  realize Zshunt
• Multiple elements in parallel should be
  distributed across the gap more or less uniformly
  around the circumference
• Zshunt must be sufficiently high impedance at
  beam current frequencies to be measured so as not
  to short circuit the gap as seen by the current
  monitor, typically gt10 ohms is acceptable
• Series RC network blocks low frequency external
  noise currents from flowing across gap and
  through monitor
• Parallel RC network exhibits lower impedance at
  high frequencies

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Classical Transformer Review

• Steady state circuit equations in Laplace
  notation
• Total magnetic flux in core
• Load side current
• Primary side loop

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Classical Transformer Review

• Simultaneous solution and use of
  , where Np and Ns are the number of primary and
  secondary winding turns respectively, yields
• In mid-band where this
  simplifies to

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Classical Transformer Review

• In the case of the beam current it is appropriate
  to replace the voltage generator by an equivalent
  current generator
• where and
  
• Substituting into Eqn. T1 with , find
• Given that , the familiar result
  is obtained.

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Noise Reduction Core on Coax
Top trace - no core Second -
5 turns of coax through core Third - 10 turns
Fourth - many turns
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Noise Signals and Spectra w/Core

• No core

• 10 turns

• Signals at 50mV/div and 40msec/div and spectra at
  10dB/div and 125 Hz/div, except no core is 500
  Hz/div.

• 5 turns

• many turns

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How Does the Core Help? To Z or not to Z?

• Noise measurements showed very low impedance
  source
• A perfectly conducting cable shield could short
  out the noise source, thereby eliminating the
  noise
• Yet apparently adding impedance to the shield
  in the form of a core also reduces the noise
• Dilemma -
• Increase shield impedance to reduce noise
  currents?
• Reduce shield impedance to attenuate noise source
  voltage?
• Solution -
• Low impedance noise is not completely overcome,
  core acts as transformer coupling equal voltage
  to shield and center conductor

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Toroid on a Coaxial Cable

• Shield and center conductor circuits, each
  looping core N times, link same magnetic flux in
  core and will therefore experience same induced
  voltage.

At frequencies above ? R/L, where R is the
shield resistance and L is the inductance of the
shield winding on the core, the end-to-end center
conductor voltage will be identically equal to
the shield voltage, in this case
Vnoise! Therefore the differential
shield-to-center voltage at both ends can be
independent of the noise voltage Note that low
shield resistance is still a good thing. It
reduces the corner frequency at which the
transformer action becomes effective! Dilemma
resolved!
The core cannot influence desired signals
propagating inside coax. With equal and opposite
in shield and center conductor currents, these
signals present no net current to core,
effectively removing the it from the picture.
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Directional Coupler
Equal signal out and along line
Zo
Zo
Zo
Zo
No signals
Zo
Zo
Zo
Zo
Forward line signal and opposite prompt signal
cancel at downstream port and opposite polarity
signal propagates backwards along line
Resulting signal at upstream port
Upstream port signal also zero in steady state
case if electrode electrical length is ½ bunch
spacing !