Update on power loss for resonator
impedance with various filling schemes
Francesco Giordano
Benoit Salvant
Acknowledgement: Elias Metral, Giovanni Iadarola, Giovanni Rumolo, Michael Schenk, Lee Carver
Last time main conclusions
From [1] we know that:
• Broad Band impedance -> The sum can be
replaced with an integral 
• Very narrow band impedance (1 term in the
sum) 
X scale log
In the meeting of the 10/04/2017 we have
assumed that in the middle case we have:
And for an ideal Gaussian filling scheme
we have obtained
[1]: Elias Métral, Diamond Light Source workshop, 30/01/2013
But why we have a quadratic
behavior only for Qr=10^5?
Target of this talk
• Follow up from last time :
• Can we understand why the interval where Alfa(Q) is varying is so huge?
What happens to alpha(Q) if the machine is always full and equipopulated?
• What happens to a real filling scheme with trains separated by empty space?
• What happens if the mode is not exactly on the beam spectrum line (offresonance)?
From now:
M=Number of bunches in the machine
d= Bunch spacing
How we compute that plot
Why the interval is so huge? The answer is in the way that we change the number of bunches.
Two options :
• Ideal way: Keep machine full and change bunch spacing (only ideal
spectrum)
• Real way or LHC like : Keep bunch spacing and fill machine progressively
(what we did last time)
Keep machine full and change bunch spacing
[1/3]
We have to vary the filling scheme without moving our mode :
• M=array([3564/22, 3564/12, 3564/11, 3564/6, 3564/4, 3564/3, 3564/2, 3564])
• d=array([dmin*22, dmin*12, dmin*11, dmin*6, dmin*4, dmin*3, dmin*2, dmin])
The values of d
are :
• 548 ns
• 299 ns
• 274 ns
• 149 ns
• 99.8 ns
• 74.8 ns
• 49.9 ns
• 24.9 ns
Alfa now is
varying in a
tight interval
Keep machine full and change bunch spacing
[2/3]
M=162
d= 548ns
M=297
d= 299ns
[Hz]
M=891
d=99.8ns
[Hz]
M=1188
d=74.8ns
[Hz]
Only ideal spectrum in frequency, no side
[Hz]
bands!
M=324
d=274ns
M=594
d=149ns
[Hz]
[Hz]
M=1782
d=49.9ns
M=3564
d=24.9ns
[Hz]
[Hz]
Keep machine full and change bunch spacing [3/3] How many main lines does the
M=324
impedance cross?
Re[Z]
d=274 ns
Bunch Spectrum
Q=10
Q=1
[Hz]
[Hz]
Q=10^3
Q=10^2
From Q=10^3 only 1
main line cross the
impedance
Consistence with
the Alfa[Q] plot
[Hz]
[Hz]
Q=10^6
Q=10^5
Q=10^4
[Hz]
[Hz]
[Hz]
Keep bunch spacing and fill machine progressively [1/3]
We have side bands in almost all the cases, just the
full machine doesn’t have side-bands
M=445
M=2227
M=891
M=2673
Machine not full Discontinuity in time, side bands in
frequency
M=1336
M=3118
M=1782
M=3564
Keep bunch spacing and fill machine progressively [2/3]
How many main lines does the impedance cross
Q=10^-2
Re[Z]
Bunch Spectrum
Q=10^-1
[Hz]
Q=10
Even when the impedance is
not crossing the other main
lines it is covering the side
bands
Q=1
[Hz]
Q=10^2
[Hz]
Q=10^3
[s]
[Hz]
Q=10^4
[Hz]
[Hz]
Q=10^5
Q=10^6
Sorry for the small plot.
[Hz]
[Hz]
[Hz]
Keep bunch spacing and fill machine progressively [3/3]
Main line contribution to the Power Loss
(Main line)/(Total Power Loss)
LHC/4
LHC*(3/4)
LHC/2
FULL LHC
Ideal Filling
Scheme
The side bands are playing a
role.
Quadratic behavior only if just
the main line is contributing to
the Power loss.
Main line contribution to the Power Loss (1/5)
[1/4 MACHINE]
Remember : only from Qr= 10^2 we are not touching the other main lines
Q=10^2
Q=10^3
Q=10^4
Q=10^5
[s]
Main line contribution to the Power Loss (2/5)
[1/2 MACHINE]
Q=10^2
Q=10^3
Q=10^4
Q=10^5
Main line contribution to the Power Loss (3/5)
[3/4 MACHINE]
Q=10^2
Q=10^4
Q=10^3
Q=10^5
Main line contribution to the Power Loss (4/5)
When just the main line is playing a role we have P=M^2
[FULL MACHINE]
Q=10^2
Q=10^3
Q=10^4
Q=10^5
Main line contribution to the Power Loss (5/5)
REAL FILLING
[FILL 4565]
2244 bunches
SCHEME
Q=10^1
Q=10^2
Q=10^3
Q=10^4
Real filling scheme-[1/4 MACHINE]-fill:4565
Q=10^2
Q=10^3
Q=10^4
Q=10^5
REAL FILLING
SCHEME
Real filling scheme-[1/2 MACHINE]-fill:4565
Q=10^2
Q=10^4
Q=10^3
Q=10^5
REAL FILLING
SCHEME
Real filling scheme-[3/4 machine]-fill:4565
Q=10^2
Q=10^3
Q=10^4
Q=10^5
REAL FILLING
SCHEME
Filling the machine movie : [1/16]
Q=10^2
Q=10^3
Q=10^4
Q=10^5
fill:4565
Bunches injected :12
Filling the machine movie : [2/16]
Q=10^2
Q=10^3
Q=10^4
Q=10^5
fill:4565
Bunches injected :120
Filling the machine movie : [3/16]
Q=10^2
Q=10^3
Q=10^4
Q=10^5
fill:4565
Bunches injected :264
Filling the machine movie : [4/16]
Q=10^2
Q=10^3
Q=10^4
Q=10^5
fill:4565
Bunches injected :408
Filling the machine movie : [5/16]
Q=10^2
Q=10^4
Q=10^3
Q=10^5
fill:4565
Bunches injected :588
Filling the machine movie : [6/16]
Q=10^2
Q=10^3
Q=10^4
Q=10^5
fill:4565
Bunches injected :732
Filling the machine movie : [7/16]
Q=10^2
Q=10^3
Q=10^4
Q=10^5
fill:4565
Bunches injected :876
Filling the machine movie : [8/16]
Q=10^2
Q=10^3
Q=10^4
Q=10^5
fill:4565
Bunches injected :1056
Filling the machine movie : [9/16]
Q=10^2
Q=10^4
Q=10^3
Q=10^5
fill:4565
Bunches injected :1200
Filling the machine movie : [10/16]
Q=10^2
Q=10^4
Q=10^3
Q=10^5
fill:4565
Bunches injected :1344
Filling the machine movie : [11/16]
Q=10^2
Q=10^4
Q=10^3
Q=10^5
fill:4565
Bunches injected :1488
Filling the machine movie : [12/16]
Q=10^2
Q=10^4
Q=10^3
Q=10^5
fill:4565
Bunches injected :1668
Filling the machine movie : [13/16]
Q=10^2
Q=10^3
Q=10^4
Q=10^5
fill:4565
Bunches injected :1812
Filling the machine movie: [14/16]
Q=10^2
Q=10^3
Q=10^4
Q=10^5
fill:4565
Bunches injected :1956
Filling the machine movie : [15/16]
Q=10^2
Q=10^3
Q=10^4
Q=10^5
fill:4565
Bunches injected :2100
Filling the machine movie : [16/16]
Q=10^2
Q=10^4
Q=10^3
Q=10^5
fill:4565
Bunches injected :2244
Off Resonance Simulation
fr=400.8MHz
Q varies from 0 to 10^6 in 15 steps
in log way
Keep the bunch spacing and fill the machine progressively :
fr
fr + 10kHz
fr + 1MHz
fr + 10MHz
Qr : 10^6
Qr : 0
Side bands contribute becomes strong very soon
Keep the machine full and change the bunch spacing :
fr
Qr : 10^6
Qr : 0
fr + 10kHz
Those plot are normalized!
fr + 1MHz
fr + 10MHz
Conclusion and next target:
• The side bands play an important role , and the way that we fill the
machine influence a lot the Alfa plot.
• We have the quadratic behavior only if we have just the main line that
is contributing to the Power Loss.
• If our assumption of
is true, in the LHC alfa is almost
never equal to 2.
• Try to understand which are the side-band that play the most
important role.
Thank you for you attention!
Appendix :
Alfa[Q] plot on the last 500 bunches
fr=400.8MHz
Q:
• 10^6
• 0
Same plots even if we don`t calculate it varying M on all its range.