Lecture 5 Normal conducting RF

Lecture 5 Normal conducting RF Dr G Burt Lancaster University Engineering

Copper Cavities In copper cavities the shunt impedance, R, should be maximised in order to achieve a high accelerating gradient. Normal conducting cavities require nosecones and a small beam pipe in order to increase the shunt impedance factor

Average Heating • In normal conducting cavities, the RF deposits large amounts of power as heat in the cavity walls. • This heat is removed by flushing cooling water through special copper cooling channels in the cavity. The faster the water flows (and the cooler), the more heat is removed. • For CW cavities, the cavity temperature reaches steady state when the water cooling removes as much power as is deposited in the RF structure. • This usually is required to be calculated in a Finite Element code to determine temperature rises. • Temperature rises can cause surface deformation, surface cracking, outgassing or even melting. • By pulsing the RF we can reach much higher gradients as the average power flow is much less than the peak power flow.

Pulsed Heating Pulsed RF however has problems due to heat diffusion effects. Over short timescales (<10ms) the heat doesn’t diffuse far enough into the material to reach the water cooling. This means that all the heat is deposited in a small volume with no cooling. Cyclic heating can lead to surface damage.

Field Enhancement • The surface of an accelerating structure will have a number of imperfections at the surface caused by grain boundaries, scratches, bumps etc. • As the surface is an equipotential the electric fields at these small imperfections can be greatly enhanced. • In some cases the field can be increase by a factor of several hundred. Elocal=b E0 2b h

Field Emission • As we saw in Lecture 3, high electric fields can lead to electrons quantum tunnelling out of the structure creating a field emitted current. Once emitted this field emitted current can interact with the cavity fields. Although initially low energy, the electrons can potentially be accelerated to close to the speed of light with the main electron beam, if the fields are high enough. This is known as dark current trapping.

Breakdown • Breakdown occurs when a plasma discharge is generated in the cavity. • This is almost always associated with some of the cavity walls being heated until it vaporises and the gas is then ionised by field emission. The exact mechanisms are still not well understood. • When this occurs all the incoming RF is reflected back up the coupler. • This is the major limitation to gradient in most pulsed RF cavities and can permanently damage the structure.

Kilpatrick Limits • A rough empirical formula for the peak surface electric field is • It is not clear why the field strength decreases with frequency. • It is also noted that breakdown is mitigated slightly by going to lower group velocity structures. • The maximum field strength also varies with pulse length as t-0.25 (only true for a limited number of pulse lengths) • As a SCRF cavity would quench long before breakdown, we only see breakdown in normal conducting structures.

RF Conditioning • As a cavity is often manufactured with a number of nucleation sites for breakdown it is necessary to condition the cavity. • This consists of a number of semi-controlled RF breakdowns, caused by increasing the RF power or pulse length very slowly over a number of days/hours. • This causes vaporisation of the nucleation sites (sharp points) just above the breakdown threshold causing a minimum amount of damage. • In theory this should allow the structure to be conditioned to any gradient but in practice every structure has a maximum field at which processing fails to be effective. • This is likely to be due to the production of secondary nucleation sites after melting the primary sites.

Maximum Gradient Limits • All the limiting factors scale differently with frequency. • They also mostly vary with pulse length. • The limiting factor tends to be different from cavity to cavity.

Nose Cones If we decrease the accelerating gap, while keeping the same voltage between the gap, the effective accelerating voltage increases due to the transit time factor. As the gap is smaller the field strengths increase, which is good where the beam is but bad elsewhere. To avoid problems we only decrease the gap near the beam. The narrowed gap region is known as a nose-cone.

RFQ Radio frequency Quadropoles are electrostatic quad’s for focussing the beam. If the electrodes are specially shaped they can also accelerate the beam. This is especially useful for low energy beams where space charge forces are large.

Standing Wave Cavities The most common type of structure is the p mode standing wave structure. This can be a single cell or multiple cells coupled together. These structures cannot have too many cells per cavity and means that for high energy accelerators many couplers are required. The cost of this is why these structures are overlooked for linear colliders like CLIC and NLC.

Phase Advance • Not all cells in a multi-cell structure will have the same phase. • The phase difference between two cells is known as the phase advance. • In a travelling wave structure the phase advance is the axial wavenumber multiplied by the iris spacing (f=kzL) • An iris loaded structure will have a group velocity of zero (standing wave) at phase advances of 0 and p.

Pi/2 structures A mode with a 90 degree phase advance has the largest frequency gap between neighbouring modes for a given cell-to-cell coupling. This makes the cavity mores stable to manufacturing, or RF source errors. If we use this mode then every 2nd cavity is empty which is inefficient. Hence we use a bi-periodic cavity where each 2nd cavity is smaller

Side coupled cavities • For multicell cavities a small aperture leads to low coupling between the cavities. • This causes there to be very small frequency separation between modes. • In order to increase the cell-to-cell coupling we can use a side cavity. • We then use a p/2 mode, where the side cell has low fields.

Bi-periodic cavity L high shunt impedance p-mode high field stability p/2-mode p/2-mode bi-periodic both ! • It’s a conventional p/2-mode cavity where alternate cavities are contracted to occupy less space, hence • Beam sees a p-mode high acceleration • RF sees a p/2-mode field highly stable Accelerating cavity Coupling cavity L a p

focusing bunching 17 KeV b = 0.28 0.48 0.68 0.88 1 1 1

Travelling wave structures • Normal conducting cavities can be standing wave or travelling wave. • In TW structures the waves phase velocity, is equal to the speed of the particles to be accelerated. • The beam will see the same phase throughout the structure. • Power can flow through all the cavities and out the other side, very low Q. • Power is also dissipated in the cavity walls.

Iris loaded structure As we saw in lecture 1, a smooth waveguide cannot be used for accelerating particles as the phase velocity is always greater than c. To obtain useful acceleration we must slow down the waves phase velocity. In accelerators we do so by using periodic iris loading. The reflections at each iris interfere with each other altering the dispersion of the structure. The dispersion becomes sinusoidal instead of parabolic.

Matched Couplers • This is not the same as S11=0 as the reflected power at one coupler could be cancelled by reflections at the other coupler, while containing a standing wave in the cavity. • In order to verify a structure is matched we must measure the fields inside the cavity. • In order for the structure to contain a travelling wave we must ensure that there are low reflections at the input and output couplers.

Floquet Theorem By measuring how the field varies between a cell and its nearest two neighbours we can use Floquet theorem to calculate the phase and reflections E = field P = cell length R = reflection coefficient y = required phase advance

Measuring Phase Advance and Match

Wakefields • For X-band structures the beampipe must be very small in radius, r, to remain cut-off to the operating mode. • The short range transverse wakefield of a cavity scales roughly with r3 (depending on the structure). • The short range wakefield cannot be damped so the structure alignment must be very precise to avoid transverse offsets. • There is a method of defeating short range wakes, known as BNS damping. • Here the electrons in the head and tail of the bunch have differing betatron wavenumbers. This can create a situation where the wake of the head periodically drive the tails oscillation and then to cancel it. (See R. Jones lectures for more details)

Cell Manufacture Specification is 5 mm. This is the best that can be achieved using CNC milling or lathe. A poor surface roughness can lead to breakdown. The machining must produce a good surface finish.

Cavity Joining Having manufactured the cells they then must be assembled to a similar precision using vacuum brazing or diffusion bonding. The joining must provide good clean intersections with a good alignment.

Lecture 5 Normal conducting RF