Coherent wave excitation in a high current storage ring. Alexander Novokhatski 58th ICFA Advanced Beam Dynamics Workshop on High Luminosity Circular e+e-Colliders October 16, 2016 Cockcroft Institute at Daresbury Laboratory, UK

Introduction We will consider a bunched beam in a storage ring. Inside a bunch all particles moving under almost identical conditions and the radiation field from each particle has same frequency spectrum, but differs in a phases depending on particles’ positions. The sum of these fields gives a coherent effect under some conditions on the bunch current distribution. We may assume that the bunch length must be smaller than the wavelength of the radiation wave in order to have approximately fixed relations between phases during the time of excitation.

Introduction The range of frequencies, were coherence becomes important may vary. We can find may be three different type of ways to have a coherent wave radiation in a storage ring.

Coherent Synchrotron Radiation The first one corresponds to synchrotron radiation, mainly to the low frequency part of the spectrum, which is independent of the particle energy. Particles of a short bunch will excite waves with a spatial coherence. The power of these waves may be many orders higher than the power radiated by a single particle. An example of coherent part of the spectrum of a 0.2 mm bunch, which “touches” 1 THz. A bunch has 4·108 particles. A critical frequency is usually much higher than a bunch frequency

Coherent Synchrotron Radiation An estimate of the total coherent power per unit length Of cause the low frequency spectrum of the synchrotron radiation is limited by the size of the beam pipe. This shielding will decrease the effect of the coherent synchrotron radiation (CSR) on the beam dynamics. The spectrum of CSR as of propagating waves can be changed and the frequency range may go to higher frequency in comparison with a bunch length due to the back reaction of these fields and distortion of the bunch shape.

Propagating waves The second type corresponds to excitation of the propagating waves due to obstacles in the beam pipe, like for example, a collimator. An energy loss of a point charge due to diffraction of its own field on an obstacle, is proportional to the particle energy. We may consider this is a high frequency part of the radiation, but we know that the low frequency part does not depend on the energy in the ultra relativistic case. Then with many particles the power will increase many times. (Same as for CSR) To fulfil the coherence condition in this case we need a smaller bunch length in comparison with a wavelength of an excited wave. 1/g

Propagating waves Simple estimate of the loss factor for an obstacle Dr in a pipe with r=a Usually these waves propagate away before the next bunch comes to this place. However these waves can be dangerous too as they can propagate long distances and be absorbed in low resistance elements like NEGs or vacuum pumps. Wake fields due to roughness surface or dielectric layer can be also include in this category, as a representative of the Cherenkov radiation. We don’t have to forget the resistive-wall wake fields and check if the beam pipe to be water cooled.

Condition for a coherent excitation: Trapped modes The third type of the coherent excitation corresponds to existence of trapped modes. This modes could exist in a cavity-like element in the beam pipe. A trapped mode has a smaller frequency than a cut-off frequency of the beam pipe for a corresponding electromagnetic field distribution (monopole, dipole, etc.). Sometimes (Murphy's Law) a frequency of a trapped mode is exactly equal to some of the beam spectrum line. The amplitude of the field in this cavity increases linear with a number of bunches passing nearby until self-saturation due to resistivity of the metal walls. Condition for a coherent excitation: resonance and

Trapped modes If electromagnetic power dissipates in the place without any outside cooling (water or air), the temperature can rise to very high level up to the melting point. We will discuss later that some cavities can be hidden outside the beam pipe but have a coupling to the beam through small holes in the metal wall or ceramic windows We can suggest that “incoherent” excitation happened when a time decay of a trapped mode is smaller than the bunch spacing And power is If the bunch spacing is equal to a mode decay time, the “coherent” power is only twice more that “incoherent”

CSR fields in the beam pipe. We found that CSR fields in a beam pipe with a rectangular (or we suggest an elliptical) cross-section, have common features with wake fields excited due to beam pipe inhomogeneity or resistivity. We believe that all these fields are solutions of Maxwell equations and must have many things in common. Some theoreticians don’t want to solve Maxwell’s equations (or may be they cannot) and they suggest some “artificial” wake functions or methods. The result is usually confusing.

CSR numerical code The CSR code, which was developed some time ago, now got new features: Calculating transverse forces coming from CSR, Space charge and wake fields. 3D particle motion Now it contains quads additionally to the bends. It includes the edge bend defocusing (usually vertical) and a gradient in the bend. The improved algorithm in the code makes it possible to simulate 20 micron or even10 micron bunches. Here we present CSR transverse forces from for SPEAR and LCLS dump magnet

SPEAR and LCLS dump magnet Beam energy 3 GeV Vacuum chamber 83 mm x 34 mm Bunch length 0.4 mm Horizontal beam size 50 micron Beam energy 13.6 GeV Vacuum chamber 25 mm x 40 mm Bunch 20 micron

Bunch and CSR fields in the beam pipe SPEAR LCLS

Bunch shape and CSR fields Integrated longitudinal force Bunch shape tail head

Energy loss averaged over a slice of a bunch SPEAR LCLS

Beam distribution on the phase plane Energy-Z tail head energy slice energy spread Longitudinal coordinate

Slice energy spread LCLS measured SPEAR

This effect is stronger We may compare with incoherent energy spread due to quantum fluctuations of synchrotron radiation Matthew Sands “Physics of Electron Storage Rings” SLAC Report No 121, 1970 382 kV for 13.6 GeV 38 kV for 3.4 GeV This effect is stronger

Horizontal kick averaged over a slice of a bunch The kick is opposite to the bend direction SPEAR LCLS

We may compare with a formula (R.Talman force without logarithm) More than two times larger than CSR force

A gradient of a vertical (SPEAR) a horizontal (LCLS) kick Tail is defocused Head is focused Similar to the wake field quad in a rectangular chamber LCLS SPEAR

Comparison with magnet edge defocusing Karl L. Brown “A first and second-order matrix theory” SLAC Report No 75, 1972 Comparable with CSR Blue line shows relative field distribution Red lines show integrated edge defocusing

A kick due to a vertical (SPEAR) or horizontal (LCLS) displacement of the beam Similar to the wake field kick LCLS SPEAR

What is better to keep in mind when designing a beam pipe for a high current machine. PEP-II experience, 3A beam current achieved. I will argue with some “researchers”, who allow to have a small gap in the beam pipe. A small gap in a vacuum chamber can be a source of high intensity wake fields, which may cause electric breakdowns. Usually a small gap in a beam pipe couples the bunch field with an outside “cavity”.

A small gap and a trapped mode between connecting flanges We suggested that the gasket (RF gap ring), which is placed in the joint between the vacuum valve and the vacuum chamber, could have dimensions that are incorrect thereby producing a very small gap. We suspected that the gap size could be of order 100 microns. The positron beam through this size of a small gap excites a cavity formed by the flange sides and the gaskets. Maximum electric field is in the gap and reach breakdown limits. When we opened the vacuum chamber we found traces of breakdowns. We cured this effect with a better design of the gap ring Wake fields due to a small 0.2 mm gap in a flange connection Electric field in the gap Breakdowns

RF seal design is very important! Almost same happened with RF Seals in the High Energy Ring

RF seal temperature jumps and an outer cavity excitation HER flanges and flexible omega seal. Red arrows show thermal radiation Measured single bunch and multi bunch spectrum

Bunch-spacing resonance in the HER bellows with broken shielded fingers HER current Bellows temperature Vacuum chamber temperature

A trapped mode when an RF seal is not installed well (a gap ring with a cut) Breakdowns traces

A quarter-wave resonance of a spoiler Somebody decided to start with a bunch pattern by 4. This pattern contains a bunch spacing resonance, which has a frequency very close to a frequency of a trapped mode: 476/4*5=595 MHz. The LER current was relatively small. What happened? Next page.

How strong wake field effect in resonance could be: melting the TI foil at the current of only 500 mA. Damage occurred during x4 running. No unusual power loss in by 2. Gouge is not caused by direct beam.

Resonance of the BPM button

HOM power from high currents Bunch Spacing Loss Factor Current Loss factor of only 0.1 V/pC “works” like a microwave Every small irregularities of the vacuum chamber become very important

Propagating waves from a collimator The shape was optimized in order to have a minimum longitudinal impedance, however the higher nonsymmetrical waves (dipole and quadrupole) have large impedance

HOM leaking from TSP heater connector The power in the wake fields was high enough to char beyond use the feed-through for the titanium sublimation pump (TSP). antenna HOM spectrum from Spectrum analyzer

HOMs go through RF screen into the NEG chamber, heat it to high temperature and destroy the pumping. RF spectrum antenna RF screens

Fight the propagating waves using shielded absorbers Tiles braised to water cooled copper support columns Ready for install

Recommendations (nothing new) Electron and positron bunches generate electromagnetic fields at any discontinuity of the vacuum chamber These fields can travel long distance and penetrate inside bellows, pumps and vacuum valves. Vacuum chamber must be very smooth. HOM absorbers must be installed in every region that has unavoidable discontinuity of the vacuum chamber Maximum attention to the RF seal designs Design of a BPM button with a cooling possibility No open (to the beam) ceramic or ferrite tiles Increase the bunch length as possible