Vadim Dudnikov* , Alexander Mikhailichenko

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Anomalous instability in CESR was discovered in mid of eighties [1]. Investigation of this instability at that time [2] did not identify the ion pumps as a source. Only later it was met that namely the ion pumps are responsible for this kind of instability [3,4]. In earlier publication [3] it was mentioned in brief, that the ions and electrons from ion pump leaking in the chamber, might be responsible for this instability. This idea was not supported however. Search for explanation continued meanwhile, and in [5] the consideration of nonlinear field which is present at the beam orbit was made. It was supposed that this nonlinear field could change the beam dynamics at the level of betatron motion. Back influence of stored beam to the ion pumps was investigated in [6]. It was suggested here, that a synchrotron radiation penetrating into DIPs, gives an additional ionization in pumping volume, and, hence, helps to pump in presence of the beam in CESR (Aluminum vacuum chamber is significantly transparent for the high part of SR spectrum [15]).

In the latest series of publications, beginning from the mid of nineties, the instability was explained by photoelectrons, trapped in the vacuum chamber in combined magnetic guide field and electrostatic field of ion pumps [7-11]. In these publications this hypothesis was investigated numerically and analytically. Reading all these publications we concluded, that the explanation with trapped photoelectrons remains the modern one up to this moment.

This explanation, however, generates a lot of questions. First of all some note was made, that there was a mistake in calculation (At the end page of [9] it was mentioned that the Author discovered a missed factor in all calculations of the beam field. It is not clear if there was any correction done for this discrepancy in [10] also). Also some questions to the model used remains. For (one) example, in calculation of motion of particles under the field of the bunch and leaking fields, the formula for electrical field gradient suggested in [6] is the following

,

where x –is a distance calculated from the wall with slots. One can see that at the exact

beam location , the gradient becomes infinite. Indeed, it must have dependence like

,

where –is a square of transverse dimension of the beam, –is a bunch length. Also not clear how gradient behaves at x=0. A lot of similar questions to the model used one can ask in the same manner.

One more comment. The trapped photoelectrons (TP) phenomena must have strong asymmetry for electron-positron beams. Really, we shall see that the SR radiation emitted by bunch reaches the wall at the same location with a quasi-static electrical field of the bunch. So the field of the bunch can strongly influence to the efficiency of photoemission.

Also, as the energy of the trapped electrons remains a few volts only, space charge forces can easily repulse the boundary electrons along the line of magnetic field, see estimations (3) and (5).

From the other hand it is well-developed description of interaction of plasma with relativistic beam in storage ring [12,13,17]. In some circumstances this kind of interaction becomes dominant in beam dynamics. The critical parameter in all these interactions is a plasma density in the region of the beam.

Strong instability of circulating beam in a circular accelerator (storage ring) driven by interaction of the circulating particles with secondary particles having compensated space charge have been predicted in [18]. In this instability a longitudinal energy of the beam transformed to the transverse oscillations by coupling with transverse oscillations of secondary particles. The condition for instability development is optimal if any mode of betatron oscillation of beam, shifted by Doppler effect to laboratory frame is equal (or close) to the frequency of secondary particles oscillation in the electrostatic potential hole of the beam:

where Q –is a number of betatron oscillation per turn, k –is a mode number for betatron oscillation, –is a frequency of oscillation of secondary particles, -- frequency of the beam revolution.

A betatron oscillation of the circulating bunches could be in resonance with plasma oscillations or Larmoure oscillation of any ions. Nonuniform plasma density has a continuous spectrum of specific frequencies and rich possibilities for resonance oscillation with a circulating bunches. Circulating bunches excited a resonance plasma oscillations and these oscillations create a fields increased a transverse bunches oscillations. This is most common mechanism for transformation a longitudinal energy of bunches to the energy of the transverse oscillations.

Interaction with other oscillation systems, such as a plasma, or any resonant circuit, also could transform energy of longitudinal motion to the energy of transverse oscillation and, hence, drive an instability. For recent situation condition for instability is also , where –is a plasma (or Larmoure) frequency, or a specific frequency of oscillation system. This instability is very strong and can be developed up to loss of beam. A threshold for these instabilities are less then for wall instabilities and these instabilities often limited an accelerator performance. The number of secondary particles for instability is low and could be accumulated in the ultra high vacuum condition.

It is well known that the beam can, in principle, accumulate the ions on the orbit. It is also known, that accumulation of the ions can be made by intense beam at the distances of the order of the bunch length [16]. The beam dynamics can be strongly affected coherently and incoherently as well [14]. In case if some gaps are present between the bunches in the beam, accumulation of the ions (and electrons) is unlikely, however.

To eliminate these instabilities, associated with accumulation of the ions, in the storage rings of Budker Institute in Novosibirsk there were used a "cleaning" by a strong electrostatic field.

A strong instability of the bunched circulating proton beam has been discovered in BINP during the development of charge exchange injection [19,20]. Strong instability of the coasting uniform circulating proton beam was described in [21]. This type of instability limited circulating beam intensity in the Los Alamos Proton compressing Ring [22].

To avoid an interaction of circulating beam with secondary ions in Synchrotron Radiation Sources (SRS) it was proposed to use positrons instead of electrons. Unfortunately, in intense positron beam the similar instability is driven by accumulation of secondary electrons, and complicated use of positron doesn’t give any advantage.

Analyzing all the facts connected with the big picture, we suggested that more likely the instability observed at CESR could be explained by beam-plasma instability, while the plasma is feed to the orbit by electrical ion pumps. So, basically, this is similar to idea, mentioned briefly in [3] (We discovered this brief mention after our own opinion was formed).

The bunch entering the magnet radiates a (synchrotron) radiation, which propagates along a straight line from the point of radiation, see Fig.1. The distance L from the entrance point to the point at the wall, where the radiation touches it, could be calculated as the following

, (1)

where R–is a bending radius of a central orbit, –is a half radial size of a vacuum chamber, see Fig.1 below.

Figure 1. Respective position of SR and the bunch at the moment, when the SR, radiated at the entrance of the magnet, touches the wall. Distance s is a measure of a slippage SR with respect to the bunch centroid.

For CESR with , , the value (1) is . The last means that only at distance 265cm from the beam entrance to the magnet, SR from the bunch touches the wall. Of cause the Pretzel mode changes this estimation.

The slippage between the particle and corresponding point at the wall defined as

. (2)

The last value is for CESR. If we take into account that the bunch length is about , we are coming to conclusion that the SR reaches the wall practically in the same region, with quasi-static electromagnetic field of the bunch is running.

The last means that electrical field of the beam has strong influence on the emission of photoelectrons. In any case, positron and electron beam, having different sign of field, must differ significantly in amount of electrons created.

Electrical field of the bunch on the distances , where — is the bunch length, N—is the bunch population, can be evaluated as the following (SI units)

(3)

where , –is unit radial vector, is the electron density. For CESR,

a single bunch circulating in a machine and having 1mA in average, corresponds to of charge. This yields electric field strength at a distance 4cm as much as

. (4)

The last figure needs to be compared with electrical field strength leaking from the pumps. The related electrical field is not more, than 0.1V/cm at the wall, where radiation touches the wall and about 100V/cm at the wall close to DIP chamber. For 10 mA of current the electrical field will be ten times bigger. So the electrical field of the beam strongly influence to the emission.

Probably the only photo- electrons could be captured are the ones radiated far apart from the beam. This is possible due to re- radiation inside the vacuum chamber.

Space charge effect for captured photoelectrons. This effect also can be estimated on the basis of formula

, (5)

where –is a charge in a cloud of trapped electrons and a –is a characteristic distance. Electrons can easily escape along the magnetic force line.

In the Penning-discharge units used in the ion pumps, a plasma potential varies from a cathode one to the one which is very close to the anode potential. In the ion pumps with positive biased anode, discharge plasma has a positive potential relative to the grounded walls of chamber. So the plasma can serve as extension of anode electrode. This anode plasma creates potential hole for electrons. Secondary electrons, knocked-out from the electrodes (walls), can oscillate in this potential hole and create efficient ionization of very low-density residual gas, what is present in a high vacuum ion pump. Slow ions created by this ionization could have a relatively long lifetime in the discharge unit before extraction to the surface. This yields a possibility for a relatively dense plasma production in the gas having very low density. Electric field is located mostly at the boundary between plasma and wall surface. Magnetic field improves a tapping of electrons. Plasma drift in the crossed fields is very efficient mechanism of the plasma transportation in a small gaps practically without plasma loss.

In devices used, the ion pumps with positive biased anodes have a common problem: if pumping discharge starts at not very low gas pressure, the intense discharge of the hollow cathode type could start in the all device volume.

At low gas pressure the plasma expansion over the volume is visibly not so easy. But all detectors of charged particles (beam position monitors, for example) yield an intense signals even at long distances from the ion pumps. Shielding the pumps by small cell grid decrease the plasma penetration from the ion pumps but don’t eliminate it completely.

Ion pump with negative biased cathodes have a good condition for electrons oscillations only inside the pump between cathodes of Penning discharges. This is because of all plasma have a negative potential relative to the grounded walls. With this type of ion pump there is no problems with the discharge expansion from the pump and was no necessity for the pump shielding.

By this reason in electron–positron storage rings at Budker Institute of Nuclear Physics (Novosibirsk) there were used the ion pumps with negative biased cathodes and grounded anodes specially designed for this reason. This design has more complicated cathode insulation but avoided a problem with a plasma expansion and influence to the beam dynamics.

A discharge triggering in the ion pump should change dramatically an electric field distribution penetrating from the ion pump to the beam chamber. Accumulated plasma have a specific shielding and resonance properties important for interaction of the beam bunches with walls and plasma.

The importance of discharge influence to beam instability have been demonstrated in experiments with a " dummy pump" in PETRA and HERA storage rings at DESY [17].

With the presence of discharge, anode shielding by grounded shield doesn’t change the triggering of beam instability by the ion pump discharge.

Ion pump with a negative biased cathode and grounded anode doesn’t influence to the beam loss.

All these effects have supported the importance of the plasma penetration to the beam chamber from ion pumps.

We suggest some experiments, which allow to find the presence of the plasma into the vacuum chamber with and without pumps on. These methods could be used even without the beam. To measure the plasma density one can use few methods.

Determination of a plasma frequency

A plasma density could be estimated by detection of plasma frequency - resonance ringing during a plasma excitation by short electric pulse and detection a signal by other probe, or during a frequency swiping in one probe and a signal detection by other shielded probe.

A propagation of the short electric pulse along the wire in the chamber could be used for simulation of the bunches interaction with a plasma.

For CESR with perimeter , the revolution frequency

Plasma frequency is a function of a density as the following

, , (5)

where –is a plasma density, m –is a mass of electron.

Plasma with has a density . For resonance with 9 trines of bunches, plasma frequency should be 9 times bigger and corresponding plasma density is 81 time higher. In magnetic field of B=2 kG a Larmoure frequency of protons is the following

,

For Argon .

So if some RF probe inserted into the vacuum chamber and is feeding with RF, one can check the absorption power as a function of frequency and, hence, define the . Turning on/off the pumps, one can identify the influence of pumps to the plasma presence in the chamber.

If two electrodes are inside a vacuum chamber, one can use a transfer function between electrodes for definition of the plasma frequency. This can made either in time or in frequency domain. One needs to prevent direct signal transduction between electrodes, what could be made by appropriate screening. For calibration again one can turn on/off the ion pumps.

An electrode with calibrated surface area S, Fig.2. A plasma density could be estimated by a saturated ion current of the Langmuir probe. An saturation ion current ( Bohm current) to the probe with a surface S, in the plasma with a density and electron temperature is

(6)

An atomic ions after ionization have very low energy as 0.1 eV, so heavy ions could have a significant propagation time in plasma. Corresponding ion current is low and flat probe as a cathode in crossed field discharge could be used for plasma density estimation

So, if the plasma is leaking from the pumps, one needs to screen the pumps by holes with smallest diameter. The hole shapes and dimensions defined by the beam dynamics. Longitudinal impedance is proportional to the round hole's diameter in a power of six, , where n –is the number of the holes per unit length. If one fix the pumping transparency, , then the impedance will behave . So one can easily reduce the impedance to any desirable value. To keep the conductivity the same when scaling the hole's diameter, one needs to reduce the wall thickness also. This is in line with requirements of technology for the holes punching. Electrical field drops as a cubic function of the hole's diameter. So small holes drastically reduce the leakage of the plasma into chamber.

A decrease of pumping holes dimensions to less than Deby radius should decrease a plasma penetration. This solution –is use very small holes in vacuum chamber for gas pumping by cryogenic wall was proposed for LHC collider for prevention of the strong gas desorbtion by synchrotron radiation.

Modification of the ion pump with negative biased cathodes and grounded anode have minimized plasma expanding possibilities to other volume.

An example of the pump with negative biased cathode is represented in Fig.3 below.

References