Fast instability caused by electron cloud in combined function magnets

One of the factors which may limit the intensity in the Fermilab Recycler is a fast transverse instability. It develops within a hundred turns and, in certain conditions, may lead to a beam loss. The high rate of the instability suggests that its cause is electron cloud. We studied the phenomena by observing the dynamics of stable and unstable beams, simulating numerically the buildup of the electron cloud, and developed an analytical model of an electron cloud driven instability with the electrons trapped in combined function dipoles. We found that beam motion can be stabilized by a clearing bunch, which confirms the electron cloud nature of the instability. The clearing suggest electron cloud trapping in Recycler combined function magnets. Numerical simulations show that up to 1% of the particles can be trapped by the magnetic field. Since the process of electron cloud buildup is exponential, once trapped this amount of electrons significantly increases the density of the cloud on the next revolution. In a Recycler combined function dipole this multiturn accumulation allows the electron cloud to reach final intensities orders of magnitude greater than in a pure dipole. The estimated resulting instability growth time of about 30 revolutions and the mode frequency of 0.4 MHz are consistent with experimental observations and agree with the simulation in the pei code. The created instability model allows investigating the beam stability for the future intensity upgrades.

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Figure 1

The first batch above the threshold intensity suffers the blowup after injection into the ring [3]. The bunch intensities of six consecutive injections in the recycler are shown on the left. The first bunch train (top) has the intensity below the threshold (dashed line), and the following injections are above the threshold. The vertical axis shows the injection position of the bunch trains in the ring. Right: turn-by-turn measurements of beam center positions of the corresponding bunch trains during the first 100 turns after the injection. Only the first batch above the threshold intensity becomes unstable.

Figure 2

Electron cloud can get trapped by a magnetic field of a combined function magnet. Image shows the field lines inside a recycler permanent combined function dipole; the gray dashed line represents the vacuum chamber.

Figure 3

Most particles hit the vacuum chamber at small angles to the normal.

Figure 4

In a combined function magnet the electron cloud accumulates over many revolutions, reaching much higher line density, than in a pure dipole. A clearing bunch destroys the trapped cloud, preventing the accumulation. Results of a numerical simulation using the pei code.

Figure 5

Electron cloud forms a stripe inside the vacuum chamber; beam center and its $2\text{−}\sigma$ boundary are shown in white. Results of a numerical simulation using the pei code.

Figure 6

Without the clearing bunch the beam of $3.6\times {10}^{12}\mathrm{p}$ blows up in about 20 turns (top); with the clearing bunch of $1\times {10}^{10}\mathrm{p}$ it remains stable (bottom). Turn-by-turn measurement of the horizontal position of the beam center.

Figure 7

Cross section of the Recycler stripline detector; dimensions in mm [17].

Figure 8

Presence of the clearing bunch reduces the tune shift between the head and the tail of the high-intensity bunch train: $5\times {10}^{10}\mathrm{ppb}$, 80 bunches. The error bars represent the spread between different measurements. The dashed lines correspond to the estimated resistive wall contributions, found by extrapolating measurements at lower intensities.

Figure 9

Simulated potential of the electron cloud, seen by the last bunch of the train of 80 bunches, $5\times {10}^{10}\mathrm{ppb}$. The absolute value of the potential is plotted as a function of displacement from the beam center. The cloud potential decreases for small horizontal displacements and increases for small vertical ones.

Figure 10

Results the of electron cloud simulation agree with the measured horizontal tune shift. Beam: $5\times {10}^{10}\mathrm{ppb}$, 80 bunches, followed by one witness bunch of $0.8\times {10}^{10}\mathrm{p}$ at various positions. The gap between the high-intensity batch and the witness is due to the rise time of the injection kickers.

Figure 11

Real and imaginary parts of impedance as a function of a mode angular frequency $\omega$. The dashed line represents the Landau damping. The modes with $\mathrm{Re}[Z(\omega )]$ below the dashed line are unstable.

Figure 12

Electron cloud wake falls exponentially with distance.

Figure 13

Simulation in pei and stripline measurements show an instability in the horizontal plane with a period of slightly less than the length of a batch and a $\text{frequency}<1\mathrm{MHz}$.