Experimental studies of the magnetized friction force

High-energy electron cooling, presently considered as an essential tool for several applications in high-energy and nuclear physics, requires an accurate description of the friction force which ions experience by passing through an electron beam. Present low-energy electron coolers can be used for a detailed study of the friction force. In addition, parameters of a low-energy cooler can be chosen in a manner to reproduce regimes expected in future high-energy operation. Here, we report a set of dedicated experiments in CELSIUS aimed at a detailed study of the magnetized friction force. Some results of the accurate comparison of experimental data with the friction force formulas are presented.

Figure 1

(Color online) Longitudinal friction force in [eV/m] vs velocity $[\times {10}^4\mathrm{m}∕\mathrm{s}]$ for three currents of electron beam. Measured data: 250 (pink dots, upper curve), 100 (red dots, middle curve), and $50\left(\mathrm{blue}\mathrm{color}\right)\mathrm{mA}$ $(B=0.1\mathrm{T})$.

Figure 2

(Color online) Longitudinal friction force in [eV/m] vs velocity $[\times {10}^4\mathrm{m}∕\mathrm{s}]$ for a misalignment angle between the beams in the horizontal direction: 0 (pink, upper curve), 0.4 (blue, middle curve), $0.8\left(\mathrm{red}\right)\mathrm{mrad}$ ($B=0.1\mathrm{T}$, $I_e=250\mathrm{mA}$).

Figure 3

(Color online) Longitudinal profiles of the proton beam for electron current $I_e=20\mathrm{mA}$ and proton current $I_p=0.6\mathrm{mA}$, shown with time steps of $0.75\mathrm{s}$.

Figure 4

(Color online) Longitudinal friction force in [eV/m] vs velocity $[\times {10}^4\mathrm{m}∕\mathrm{s}]$ for different magnetic fields with parameter $\alpha =1.3$ (pink dots, upper curve), $1.0$ (blue), $0.9$ (red), $0.8$ (green, lower curve) from top to bottom, respectively.

Figure 5

(Color online) Longitudinal friction force in [eV/m] vs velocity $[\times {10}^4\mathrm{m}∕\mathrm{s}]$ with correctors on (blue dots, upper curve) and off (red dots) for $I_e=100\mathrm{mA}$ and $B=0.06\mathrm{T}$.

Figure 6

(Color online) Longitudinal friction force in [eV/m] vs velocity $[\times {10}^4\mathrm{m}∕\mathrm{s}]$ for electron currents of 50 (blue, lowest set of data), 100 (red), 250 (pink), $500\mathrm{mA}$ (black, highest set of data) and a magnetic field in the cooling solenoid $B=0.1\mathrm{T}$.

Figure 7

(Color online) Measured friction force (points) in [eV/m] vs velocity $[\times {10}^4\mathrm{m}∕\mathrm{s}]$ for an electron current of $500\mathrm{mA}$ $(B=0.1\mathrm{T})$ and fitted curve based on Eq. (3) with an additional contribution to the effective velocity from the space charge of the electron beam.

Figure 8

(Color online) Longitudinal friction force in [eV/m] vs velocity $[\times {10}^4\mathrm{m}∕\mathrm{s}]$ for electron current of $300\mathrm{mA}$ $(B=0.12\mathrm{T})$. Experimental data: dots; solid line (black): the force averaged according to Eq. (4) with fixed coefficient $C=1∕\pi$ and fitted effective velocity $4000\mathrm{m}∕\mathrm{s}$; dashed line (green): single-particle force according to the Eq. (3) with corresponding effective velocity $4000\mathrm{m}∕\mathrm{s}$.

Figure 9

(Color online) Measured force (dots) in [eV/m] vs velocity $[\times {10}^4\mathrm{m}∕\mathrm{s}]$ for an electron current of $300\mathrm{mA}$ $(B=0.12\mathrm{T})$ and the fitting curve according to the Eq. (4) with an experimentally determined effective velocity.