1. Longitudinal instability study of the MAX-IV 3GeV ring
The impact of a small-emittance lattice on the beam stability
Thomas Friedrich Günzel
XX ESLS Berlin
19th November 2012
This work is result of a collaboration of ALBA with MAX-IV
for the design of the MAX-IV vacuum system
Also Soleil is involved in the project.
Speaking of MAX-IV I always mean the MAX-IV 3GeV ring
Thomas Günzel, XX ESLS

2. Outline Motivation of the subject
Longitudinal instability threshold criterion
Heat load
Overview of the vacuum system
Standard cavity tapers
Landau cavity tapers
VC1 + VC2 (the 2 chambers downstream of the ID)
Bellows
Flanged BPM block (w/o buttons)
BPM buttons
Conclusion
Thomas Günzel, XX ESLS

3. The need of an adapted vacuum system and its consequences
In order to achieve stronger magnetic fields on the beam axis
the magnetic poles have to be closer at the beam path than for
already existing synchrotron light sources.
In order to achieve this the vacuum chambers have to be
significantly smaller.
In order to maintain good vacuum NEG-coating has to be
applied around the whole the circumference (local excep-
tions possible).
Unfortunately, a smaller vacuum chamber increases the impedance
Zτ ~ b-3 for trans. resistive wall and Rs~ b-8 for the long. shunt
impedance of a small discontinuity (S.Kurennoy).
Large impedance
the coupling impedance (long. and trans.) of the
vacuum system and the related intensity-dependent
instabilities have to be studied thoroughly.
Only longitudinal effects are studied.
Thomas Günzel, XX ESLS

4. The impedance of the adapted vacuum system
also requires an adapted RF-system
Moreover, the vacuum pipe cut-off frequency is very high (~c/b)
therefore the impedance has to be studied up to 10.4GHz.
Therefore, a rather fast decaying beam spectrum form factor
is beneficial for the beam stability.
This, however, can only be achieved by significant bunch lengthening.
Machine parameters of MAX-IV:
Compared to many other SLSs
the synchrotron tune is rather low.
Therefore the bunch length w/o HC
is already factor 2 longer than
in most other SLSs.
Additionally Landau damping is created by harmonic cavities (HC) => στ=187ps
Thomas Günzel, XX ESLS

5. Application of the threshold criterion for LCBIs
threshold criterion based on Landau damping (according to Bisognano, Krinsky, Bosch)
It needed to be extended up to the cut-off frequency of 10.4GHz.
mode (resonance) by mode (resonance)
this way the instability risk is overestimated.
“counter term”
Coupled bunch mode spectrum μ
bessel 187ps
gauss 20ps
gauss 40ps
A special form factor(bessel) has to be used, it decreases more slowly with frequency
Thomas Günzel, XX ESLS

6. Heatload computation Calculation of the loss factor:
: FT of the stretched bunch profile
10-10 1
GHz
difficulty: κl very sensitive to noise at low
frequency and at high frequency nothing is left
incoherent loss:
homogeneous filling: P[W]=κl [mV/pC]x 2.5
The value of the losses strongly depend on the frequency of the 1st
resonance, therefore for most geometries the loss is negligible small.
Coherent loss does not need to be considered in most cases.
Thomas Günzel, XX ESLS

7. Vacuum system overview
Schematic illustration of an MAX-IV achromat
Vacuum system overview
1 Inj 3 2 20 19 18 17 16 15 14 13 12 11 9 10 8 7 6 5 4 Dk Mk E1 E5 RF L LK RS VP
20 achromats connected by 5m long straight sections
Each achromat consists of 7 magnet
cells (integrated girder magnet design)
Vaccum system consists of 10 standard chambers (VC straight section)
standard chamber : circular of 11mm radius
23 different elements simulated
only a selection will be shown
But no Low-gap chambers
design not finished yet
For this presentation only 6 selected elements will be discussed.
Thomas Günzel, XX ESLS

8. Simulations carried out with GdfidL (W. Bruns)
wake field (up to 8m) and subsequent coupling impedance computation (T-domain)
bunch length 4mm and step size 0.2mm
eigen mode computation in most cases up to 10.4GHz (F-domain)
computation of the shunt impedance and quality factor of the found
modes by material assignment to different parts of the geometry (some
simplifications applied)
The wake field computation was done
to support the eigen mode computation
to provide an input for tracking simulation in long. phase space
(check on the microwave instability)
The data is shown in a logarithmic presentation of coupling impedance and the
shunt impedance of each mode. The shunt impedance is multiplied by the quantity
of the corresponding element in the ring.
On top of it the threshold curves for LCBIs are plotted for
1)20ps bunch length, 2) 40ps bunch length and 3) additional Landau damping.
Both scales (left: coupling impedance and right: shunt impedance) are identical
Thomas Günzel, XX ESLS

9. Standard cavity taper(ONLY TAPERS)
The distance between the up- and downstream taper is strictly respected.
const. drift tube between the tapers
pipe diameter 50mm, cut-off f=4.59GHz
127mm
152mm
Spectrum 4.59GHz<f<9.16GHz
Shunt impedance rather large
Heatload problem non-existing
No instability risk for MAX-IV thanks to Landau damping and long bunches
Thomas Günzel, XX ESLS

10. Landau cavity taper
Landau cavity taper pair (between both a constant drift tube is assumed)
Close-up view of the upstream taper
The upstream taper is only 39.3mm long due a corrector upstream
The downstream taper is the same than in the precedent geometry.
In order to start from the same pipe cross section the bellows had
to be taken into the simulation.
Thomas Günzel, XX ESLS

11. Landau cavity taper con’t
f=5.57GHz
Compared to the first taper pair the shunt impedance is larger,
the distance to the Landau threshold curve is smaller
Thomas Günzel, XX ESLS

12. VC1- VC2 2 vacuum chambers directly downstream of the insertion device
VC1 passes photon beam through the antechamber to the 2nd chamber
VC2 separates photon beam from electron beam
VC2 contains a crotch absorber and accessory similar to the those of the SLS.
both have varying cross section to adapt to electron and photon path
Thomas Günzel, XX ESLS

13. VC1- VC2 con’t
f=2.16GHz
Rs=77.4Ω
Inspite of moderate shunts impedances the overall effect (19x in the ring) of this element is similar to the cavity tapers
for one mode the comparison shunt to threshold is worse than for the cavity tapers
Thomas Günzel, XX ESLS

14. Typical modes in MAX-IV chambers
f=8.147GHz
f=4.35GHz
Rs=10.7Ω
f=9.483GHz
Rs=62.4Ω
typical modes:
in a pump
kind of TE modes
in the BPM block
Thomas Günzel, XX ESLS

15. Standard bellows 15 elements (there are more of diff. type)
characterized by the pump slits and
the jump between the fingers and the
sleeve
The discontinuity has triangular shape
According to Kurennoy’s theory of
discontinuities:
Ψ susceptibility
discontinuity in the beam pipe 2b e- A
close to the cut-off at 9.16GHz
Thomas Günzel, XX ESLS

16. Standard bellows con’t
Rs=167Ω
f=9.07GHz
resonance
rather close
to the cut-off
If there are many bellows in the ring such a resonance can become rather dangerous (in MAX-IV the number is limited though)
Thomas Günzel, XX ESLS

17. BPM block sandwiched by a double flange
resides on each side of the majority of the vacuum chambers (120x)
taper (11->12.5)
taper (12.5->11)
absorber protects
BPM block
bellow
(w/o buttons)
flange
the taper pair is necessary
to protect the BPM block
from synchrotron radiation
This geometry allows modes to get
trapped not only in the flanges, but also in the swelling.
Thomas Günzel, XX ESLS

18. BPM block sandwiched by double flange con’t
main
double resonance
of in total 98Ω
f=9.82GHz
Rs=3.18kΩ
f=9.34GHz
Rs=466Ω
At f=9.82GHz a mode exists whose shunt is only a factor 3 below threshold.
Thomas Günzel, XX ESLS

19. Standard BPM button large shunt impedance Rs = 105Ω
no external load
no radiation loss
considered
large shunt impedance Rs = 105Ω
the ALBA button only Rs =15.7Ω
The high shunt is not a risk for MAX-IV because the resonance frequency is so high.
Thomas Günzel, XX ESLS

20. Standard BPM button con’t
Understanding the high shunt impedance Rs=15.7Ω).
we use Kurennoy’s theory on “impedance of discontinuities”.
round pipe of MAX-IV (dependency on b very strong)
rectangular pipe (ALBA) a>b
susceptibility of the discontinuity (button)
evaluation of both formulas for MAX-IV and ALBA beam modes:
Rs=5.8e-7Ω for MAX-IV (round pipe)
ALBA pipe as rectangle
Due to the pipe geometry the MAX-IV shunt impedance is larger.
or: due to asymmetric position in rec. pipe the Rs of the ALBA button is rather small.
Thomas Günzel, XX ESLS

21. Standard BPM button con’t
Simulation experiments:
ALBA button in MAX-IV
chamber
Rs=370Ω
no external load
no radiation loss
considered
This result supports the analytical calculation
Thomas Günzel, XX ESLS

22. Conclusions
The comparison of the time-domain to the frequency domain calculations
allowed a very detailed stability study of the MAX-IV 3 GeV ring.
Landau damping combined with bunch lengthening makes sure that the vacuum
design of MAX-IV 3GeV ring is safe.
Although not shown here, cavity modes were found which don’t fulfill threshold
criterion.
The wake field could be computed for almost the whole ring (low-gap chambers
missing though) These data provide perfect input for the tracking simulations
(R.Nagaoka, Soleil)
Due to the long bunch length for all elements except the cavities heat load
is not an issue.
Several important modes just below the cut-off frequency were observed as
it is predicted by the theory of Kurennoy. Although below the threshold, they
could become dangerous if the made assumptions (RF, #elements) are changed.

23. Thank you for your attention
Acknowledgement to my collegues:
D. Einfeld, E.D’Amour, J.Pasquaud, M.Grabski and P.Tavares
Thank you for your attention

24. 100MHz cavity (back-up slide)
Simulation w/o tapers
linear representation
overlay of eigenmode Rs
and coupling impedance
scales not the same
logarithmic representation
scales the same for Zl and Rs
mode spectrum
only up to 1.2GHz

25. Landau cavity (back-up slide)
Simulation w/o tapers
Thomas Günzel, XX ESLS