1. Positive Ion Current – Hot Coulomb Explosion?
Magnus Johnson
Uppsala University
My name, where I come from, title of presentation

2. Magnus Johnson, Uppsala University
Outline
First observations
Analytical calculations
Fit of theory to data
Recent and ongoing measurements
Outline: What I will talk about
Magnus Johnson, Uppsala University

3. Magnus Johnson, Uppsala University
First observations
First measurements spring/summer 2006.
FC signal after RF-breakdown viewed by oscilloscope.
Timescale ~ 50 µs.
FC signal [V]
After a RF breakdown in accelerating structure there will be a (fast) burst of electrons (ns scale) dark current,
sometime followed by a slower burst of positive particles.
In the plot: fast e- signal, followed by overshoot (electronics). After e- signal comes (slow) positive signal.
Time [us]
100
Magnus Johnson, Uppsala University

4. Magnus Johnson, Uppsala University
Set-up
RF in
RF out
Upstream signal
(to scope)
Downstream signal
(to scope)
Accelerating structure
Basic set up.
Upstream and downstream refers to where the beam in the structure would be.
‘Upstream’ FC
‘Downstream’ FC
Magnus Johnson, Uppsala University

5. Analytical calculations
One possibility: Ion originates from Coulomb explosion of spherical, homogenous distribution of ions.
Last & Jortner, Phys. Rev. A 71 (2005): dN/dE, not including motion due to temperature T.
Ziemann, NIM. A 575 (2007): dN/dt, including motion due to temperature T.
dN/dt = f ( N0, α, ts )
N0 = number of particles in sphere
α = RMS width of velocity distribution due to thermal motion (T)
ts = arrival time of fastest ions from cold distribution.
Consider the possibility that the ions originate from a Coulomb explosion of a spherical homogenous distribution of ions.
Analytical calculations of Coulomb explosion been made previously, (for example by Last & Jortner).
Last & Jortner calculated the energy spectrum from a Coulomb explosion, not taking the thermal velocity of the ions into consideration.
Ziemann: Arrival time spectrum, also considering the thermal velocity of the ions into consideration.
According to the Ziemann theory the arrival time spectrum can be described by a function of three parameters.
-N0 (total number of particles in sphere)
-alpha (allows for determining the temperature!)
-ts (arrival time of the first ions from a distribution without thermal motion)
Magnus Johnson, Uppsala University

6. Magnus Johnson, Uppsala University
Theory Fit
Fit to data allows for determining:
temperature of ion sphere,
number of particles in sphere,
but only if
the distance to the detector
the mass of the ions
the number of ions reaching the detector is well understood (solid angle coverage, acceptance of FC etc, etc…)
…are all known!
Magnus Johnson, Uppsala University

7. Magnus Johnson, Uppsala University
First fit: 2006 data
Time [us] Mo 40
Time [us]
100 Cu
FC signal [V]
FC signal [V]
Calculated T:
Mo: Order of [K]
Cu: Order of [K] resp [K]
(Assuming detector at 0,1 m distance,
Mass of ions = mass of Mo resp. Cu ions)
Fit made with MATLAB tools.
Left: Molybdenum.
Black dots: measured data. Green lin = fit of theory.
Right: Copper. As before the black dots is measured data. Red respectively green line is fit of theory to data.
It was observed that there was two peaks -> try and fit the sum of two independent Coulomb explosions.
Calculated T.
Mo boils at 5830 K
Cu boils at 2855 K
1 J is enough to vaporize copper corresponding to a sphere with radius 0.3 mm.
NB! T is not probably not accurate, but it is encouraging that the values are reasonable.
Magnus Johnson, Uppsala University

8. Magnus Johnson, Uppsala University
2006 Data Limitations
Not many (11 Cu and 2 Mo)
Set-up not well known
Acceptance of FC?
Distance to FC?
Signal attenuation?
→ New measurements needed!
Magnus Johnson, Uppsala University

9. Magnus Johnson, Uppsala University
Recent Measurements
Measured signal
Negative signal!
Explanation:
secondary e- emission.
→ signal inverted if ion causes more than 1 electron emission (re-absorbed by FC)
→ Fit the inverted signal
Calculated T=order of 100 [kK]
Possible solution: put a bias voltage on the FC!
FC signal [V]
Time [us]
100
Inverted signal
Data taken in the same way, but with Aqurirs cards instead of scope.
NB! N0 is only a amplitude factor, so if there is the same amount of e- for every ion N0 can not be measured, but alpha and ts will remain the same!
NB! 100 kK seems like a high temperature, but is actually very close to the temperature needed remove one electron from a copper atom!
Again, this is very preliminary results, but the order of magnitude of temperature is at least not totally off!
FC signal [V]
Time [us] 90
Magnus Johnson, Uppsala University

10. Magnus Johnson, Uppsala University
Ongoing Measurements
Right sign from FC ion part.
Need to add amplifiers. (Attenuation due to splitting signals several times).
Need to add resistive power splitters (use BNC-T now → possibly reflections).
Require calibration
Need to vary bias voltage, RF pulse energy etc in order to increase understanding.
Suggestions for future set-up (to use in two-beam test-stand):
Dipole magnet (separate ions from electrons, measure energy)
Silicon detector instead of FC (accurate measurement of N0)
First measurements: just collecting data with the machine set to conditioning and breakdown rate measurements. Hopefully we will make some specialized ion current experiments next week.
The FC used are not an optimal detector for ions. May well not be possible to measure number of particles!
Still doing analysis, but have some GENERAL OBSERVATIONS!
Signal MOSTLY seen in one of the FC. Sometimes seen in both (delayed). Sometimes stronger signal in the other FC.
Bias voltage might affect arrival time spectra.
Magnus Johnson, Uppsala University

11. Magnus Johnson, Uppsala University
Magnus Johnson, Uppsala University

12. The Arrival-time Spectrum of Hot Coulomb Explosions
Arrival time spectrum (due to EM force and thermal motion):
N0: Number of particles in initial sphere,
ρ: the number density of initial sphere,
R: the radius of initial sphere.
3 free parameters in this model: *
α: RMS width of thermal velocity distribution divided by vs,
k: Boltzmanns constant,
T: the temperature of the initial charge distribution,
m: the mass of the ions. *
ts: arrival time of the fastest ions from cold distribution,
L is the distance from the detector to the Coulomb explosion,
vs is the velocity of the fastest ions from a cold Coulomb explosion *
Magnus Johnson, Uppsala University

13. Magnus Johnson, Uppsala University
HV Bias Box
FC (left) sees a high-pass filter with cut-off frequency of 1.5 Hz
HV (bottom) sees a low-pass filter with cut-off frequency of 1.5 Hz
Signal out (right) is decoupled by a capacitance, and has 0 bias voltage.
Magnus Johnson, Uppsala University

14. Magnus Johnson, Uppsala University
Signal Schematic
Magnus Johnson, Uppsala University

15. Magnus Johnson, Uppsala University
Cu and Mo properties
Boling point
Cu: 2855 [K]
Mo: 5830 [K]
Heat of vaporization
Cu: 4.75 [MJ/kg]
Mo: 6.83 [MJ/kg]
Energy per RF pulse ~ 1 [J]
enough to vaporize order of 1 mg material
1 mg copper corresponds to a sphere with radius R=0.3 [mm]
Ionization energy
Cu: Eion = [eV]
Mo: Eion = [eV]
Temperature needed to ionize Cu: Eion=(3/2)*kB*Tion → Tion = 2*Eion/(3*kB) ≈ 100 [kK]
Magnus Johnson, Uppsala University

16. Magnus Johnson, Uppsala University
Abstract
RF-breakdowns in the CTF accelerating structures have been observed to be accompanied by a fast burst of negative particles (electrons, ns scale), and a slower burst of positive particles (possible ions, us scale). One possible source of the slow ion burst is a hot coulomb explosion. A theory which predicts the arrival time spectrum of particles from such an event have been derived. Previously taken data from CTF have been fitted to this theory. Current and future measurements of the ions are discussed.
Magnus Johnson, Uppsala University