2

3eHe

e nNnnNdt

dn

Hydrogen Recombination

Time (µs)

RF E

nvel

ope

(V)

Here 0dt

dne

So 2enN

We get2en

N

Calculated from # of protons per bunch

Calculated from energy loss (voltage drop) in the cavity

hrn

N

e

22

I am actually calculating the number, not

number density, so to find the real betacmh

cmr

66.1

1.0

Model

Time (µs)

RF E

nvel

ope

(V)

V0

V

fndwPo e

cR

VVVPo

0

fdwR

VVV

fdw

Pon

ce

0

fhV

f

Edw

21

2317

21

2317

Pr

10428.1

Pr

10428.1

hrn

N

e

22mod,

Procedure

1. Determine if RF pulse after was recorded (yes for >= July 25th)2. If yes, use RF pulse after to find cavity resistance, if no, use pulse during beam3. Read in pickup, downstream toroid, pickup pulse after (if it exists)4. Calculate cavity resistance5. Calculate beam intensity6. Determine parameters of interest (i.e. recombination rate)

Reading in the Data

1. Average first 500 pts (100ns), then subtract from raw data

2. Take absolute value of raw data3. Take a moving average over x data points,

based on frequency, trying to sample over an integer number of cycles

4. This is the envelope, and will be used for further analysis

1. Average first 500 pts (100ns), then subtract from raw data

2. Take absolute value of raw data3. Take a moving average over x data points to

filter out background noise

Pick 424 points

Pickup Signal Toroid Signal

424 points = good

422 points = better

Determining Beam Intensity

1. Find the average of the first 500 points (100 ns) from the toroid, this is the offset2. Find the minimum voltage after t=03. Subtract offset from minimum, that is the signal4. Calculate current = V / 50 Ohm * 10 turns5. Calculate charge = I * 7.5 µs6. Calculate # of protons per pulse = c / (1.6*10^-19 C/p)7. Calculate # of protons per bunch = #PpP / (7.5 µs * 200 MHz = 1500)

V0

V

Determining Cavity Resistance

1. Pick the maximum voltage after t=40 µs2. Select data from this point to the end3. Drop the first 5000 points (1µs)4. Fit remaining data with an exponential of the form

5. τ = 1 / a3 (in units of µs)6. Rc = τ * 10-6 / C (capacitance of cavity)

7. This is done, if possible, to the RF pulse after beam, as electrons are still present in the cavity when the klystron turns off

)(21

43 ataeaaty

LfC

22

1

L = 24.13 nH

Typical values: 1.55 MΩ (pulse after) 1.66 MΩ (pulse during)

Determining the Voltage Drop in the Cavity

1. Oscilloscope triggers on linac pulse2. Define the start of the beam to be when the toroid signal drops below 1 mV (this is pretty

accurate – the noise is much less than this)3. The relative cable delay between toroid and pickup signals (48.07 ns) is taken into account4. Find this t0 in the pickup signal and the corresponding voltage5. Average over the previous 500 points (100 ns), call this the starting voltage, V0 6. Find the minimum voltage then average over 250 points (50 ns) on either side, call this the

min voltage, V7. Remember, at this point

Time (µs)

RF E

nvel

ope

(V)

V0

V

0dt

dne

Values That Are Calculated

N is the # of electrons per second, and is calculated from the # of protons per bunch, the ionization loss for protons in hydrogen, the gas pressure, and the bunch length (5 ns)

en is the # of electrons in the cavity, and is calculated from the power loss in the cavity

, the energy loss per cycle per electron (dependent on the cavity voltage, pressure and frequency), and the RF frequency

cR

VVVP

0

fdw

Pne

hrn

N

e

22

The temperature of the gas is also estimated, by

Where in our case, the RMS KE of the swarm is approximated by Heylen as

TkKE B2

3

71.0

357.0

P

EKE

Example Data SetDate Time Tau (µs) R (Ω) #p per bunch #e per bunch Power (J) dw (J/cycle/e)2011_08_08 11_40_55 2.867241 1.757E+06 2.04E+08 3.35E+11 8306.809 1.37E-182011_08_08 11_41_56 2.86111 1.754E+06 2.06E+08 3.39E+11 8262.911 1.36E-182011_08_08 11_42_57 2.863663 1.755E+06 2.1E+08 3.44E+11 8146.036 1.33E-182011_08_08 11_43_58 2.862209 1.754E+06 2.05E+08 3.37E+11 8331.708 1.36E-182011_08_08 11_44_59 2.862045 1.754E+06 1.93E+08 3.17E+11 8285.927 1.37E-182011_08_08 11_46_01 2.866242 1.757E+06 2.01E+08 3.31E+11 8250.832 1.36E-182011_08_08 11_47_02 2.860478 1.753E+06 1.99E+08 3.27E+11 8245.441 1.37E-182011_08_08 11_48_03 2.857276 1.751E+06 1.96E+08 3.21E+11 8433.518 1.41E-18

#e in cavity (ne) k (s^-1) β (cm^3 / s) T (K) dw model ne model k model β model7.55E+12 1.18E-06 6.13E-08 1386.356 1.47E-18 7.06E+12 1.35E-06 7.02E-087.58E+12 1.18E-06 6.15E-08 1380.337 1.45E-18 7.09E+12 1.35E-06 7.04E-087.64E+12 1.18E-06 6.15E-08 1366 1.42E-18 7.14E+12 1.35E-06 7.04E-087.61E+12 1.16E-06 6.07E-08 1383.045 1.46E-18 7.11E+12 1.33E-06 6.95E-087.53E+12 1.12E-06 5.82E-08 1386.298 1.47E-18 7.04E+12 1.28E-06 6.67E-087.54E+12 1.16E-06 6.06E-08 1382.486 1.46E-18 7.05E+12 1.33E-06 6.94E-087.48E+12 1.17E-06 6.1E-08 1387.594 1.47E-18 6.99E+12 1.34E-06 6.98E-087.45E+12 1.16E-06 6.04E-08 1405.714 1.51E-18 6.96E+12 1.33E-06 6.92E-08

10MV/m, model top

20MV/m, model top

30MV/m, model top

30.1MV/m, model top

10, 20 & 30.1 MV/m were all taken on 7/15, 30 MV/m was taken on 8/8

500psi, model top

800psi, model top

950psi, model top

10, 20 & 30.1 MV/m were all taken on 7/15, 30 MV/m was taken on 8/8

Low intensity, model top

Medium intensity, model top

High intensity, model top

High intensity, 30.1MV/m, model top

10MV/m, model bottom

20MV/m, model bottom

30MV/m, model bottom

30.1MV/m, model bottom

10, 20 & 30.1 MV/m were all taken on 7/15, 30 MV/m was taken on 8/8

500psi, model bottom

800psi, model bottom

950psi, model bottom

Low, model bottom

Medium, model bottom

High, model bottom

30.1MV/m, High, model bottom

10, 20 & 30.1 MV/m were all taken on 7/15, 30 MV/m was taken on 8/8

10, 20 & 30.1 MV/m were all taken on 7/15, 30 MV/m was taken on 8/8

10MV/m, model top

20MV/m, model top 30MV/m, model top

30.1MV/m, model top

500psi, model top

800psi, model top

950psi, model top

10, 20 & 30.1 MV/m were all taken on 7/15, 30 MV/m was taken on 8/8

Low intensity, model top

Medium intensity, model top

High intensity, model top

30.1MV/m, high intensity, model top

10, 20 & 30.1 MV/m were all taken on 7/15, 30 MV/m was taken on 8/8

10MV/m

20MV/m

30MV/m

30.1MV/m

500psi

800psi950psi

Low intensity

Medium intensity

High intensity30.1MV/m, high intensity

10, 20 & 30.1 MV/m were all taken on 7/15, 30 MV/m was taken on 8/8

Intensity Pressure Gradient β (*10^-8 cm^3/s) Std. Dev. (*10^-8 cm^3/s) %

Low* 950 30 5.73869 0.647824 11.3

Medium* 950 30 9.35292 0.882056 9.4

High* 950 30 6.06686 0.10592 1.7

High 950 30.1 5.48551 0.278517 5.1

High 950 20 8.60451 0.225403 2.6

High 950 10 20.2042 1.52449 7.5

High 800 20 6.76041 0.208048 3.1

High* 500 20 2.37975 0.411647 17.3

Summary