About the damage mechanisms of thin targets exposed to high-power particle beams

Thin targets, in the forms of wires, stripes, or foils, are often used in accelerators to measure the properties of particle beams. Motivations for a small thickness, typically between several and hundred micrometers, are diverse. The minuscule diameter of a wire allows for precision measurement because it is probing a small fraction of the beam’s transverse profile. In case of high-power beams, the important rationale is also a small energy which beam deposits in the target and a good cooling because of a large surface-to-volume ratio. In certain beam conditions, the temperature of the target is still very high and leads to wire damage. This paper presents detailed analysis of ductile breakage of a molybdenum wire and gives a short overview of other damage mechanisms for various materials.


Introduction
Thin wires, stripes or foils, are often used in accelerators to probe the particle beams or to strip ions to different charge state.They are also used in electrostatic septa magnets, to separate space with field from a field-free region.Here we focus on wires used in wire scanners and secondary electron monitors (e.g.SEM grids), where they serve as thin targets to probe the transverse beam profile.Nevertheless, the presented findings can be also useful for other applications.
The small thickness of these targets has the following consequences: • thinner objects have larger surface-to-volume ratio; the main cooling processes are determined by the surface while heating depends on the volume, therefore a larger surfaceto-volume ratio leads to lower temperature; • the heating process is mainly due to particle interaction with target electrons; for thin targets some of the electrons are kicked out effectively leading to the energy deposition significantly smaller than expected from the Bethe-Bloch formula; • thinner objects lead to smaller beam perturbations; wire scanners in high-energy proton machines are almost non-intercepting devices.
Limiting the temperature of the wire is crucial because of the damage but also because the thermionic electron emission at high temperatures can dominate the secondary electron emission process, which is often the measured signal.
The lower limits to the thickness of the wires and foils are related to the way they are handled and mounted.For practical reasons it should be easy to manipulate them without special equipment.In case of carbon fibers the manual handling becomes very difficult for wires thinner than 10 µm.There are two ways of reading the signal from thin target detectors, either by above-mentioned secondary emission current or by measurement of the flux of the secondary particles shower generated in the wire.

Materials
Tungsten, molybdenum and carbon fibers currently dominate material choice for thin targets in high-power beams.It is because of a very good combination of thermal, mechanical and electrical properties of those materials.Other materials are beryllium, silicon carbide, tantalum, quartz and titanium.Ongoing studies evaluate the use of high-temperature resistant ceramic materials or carbon nanotubes (CNT) [1].Some of the critical parameters of the materials are shown in Table 1.Strength stands for an approximate ultimate tensile strength for wires of the relevant diameter.The heat capacity and the strength values are given at room temperature.Final choice is a compromise between various parameters of the material, beam, RF-environment and the scanner itself (acceleration forces, required prespring).

Heating and cooling
The main wire heating mechanisms are coupling to the RF fields generated by the beam or leaking from the cavities, and direct interaction with the beam particles.In the first case, the maximum temperature depends on RF field and is reached at various positions along the wire.In the second case, the heating pattern follows the beam profile.The Bethe-Bloch formula states that the heating is proportional to Z • ρ, so low-Z and low-density materials make better targets.Therefore, researchers investigate targets made of carbon nanotubes [2].

Cooling
The two principal cooling mechanisms are radiative and thermionic emissions.The heat capacity of the wire plays an important role for the fast scan of high-brightness beams [3].Due to small cross section of the wire, the conductive cooling is usually negligible.

Ductile damage
The scanner studied here [4] is located on the 590 MeV proton beam of Ultra Cold Neutron beamline at the PSI High Intensity Proton Accelerator facility [5].The beam is produced in wire stretched on a C-shaped fork with a prestress of approximately 400 MPa.The scan speed is 6 cm/s.
The scanner was installed in 2022 and the wire broke in the during the commissioning at scan number 52. Figure 1 shows an electron microscope image of the broken end with signs of plastic deformation.The stress imposed on the wire exceeded its ultimate strength, causing necking at the weakest point.The thinned zone is about 10 µm long, much shorter than the beam size.The beam profile observed during one of the scans is presented in Fig. 2. It shows a clear contribution of thermionic emission on top of the secondary electron current.A simulation of both currents, using pyTT code [6], is overlapped with data.The simulation slightly underestimates the secondary emission current, which could be partly due to the fact that it assumes a Gaussian beam, while in the observed profile the tails are cut.The dotted line represents the simulated maximum temperature profile.The duration of the thermal pulse is less than a second.
The ductile damage observed in Fig. 1 means that the wire was in conditions in which the prestress repeteadly exceeded the flow stress (Y f ), i.e. the value of stress necessary to keep the material flow.Zerilli-Armstrong model [7] is used to parameterise flow stress as a function of temperature, strain, and strain rate.The parameters of this model for molybdenum can be found in [8]. Figure 3 shows the evolution of flow stress as a function of temperature for various strain rates.The green curve corresponds to the approximate duration of the heat pulse during

Thermionic emission evolution
Figure 4 presents the evolution of the thermionic emission current during the series of scans with a beam intensity of 1.8 mA.Earlier scans can be neglected, because they were mostly done without the beam.Despite constant beam conditions, the thermionic current increases from negligible at the beginning of the series to about 1.5 times the secondary current at the end.It is likely the result of structural changes caused by thermal cycling and repeated flow stress exceedings.
Comparison of electron microscope images taken along the wire, seen in Fig. 5 reveal surface cracks created in the zone affected by the beam, but before the breakage point.These cracks can potentially affect two properties of the wire: emissivity and work function.
The impact of plastic deformation on work function was discussed, for example, in [10], where a decrease of approximately 0.2 eV was found in plastically deformed aluminum and copper, however, no literature on the behavior of work function under thermal stress was found.The red curve in Fig. 4 shows the decrease in the work function required to explain the observed thermionic emission.A decrease of emissivity could also play a role.

Countermeasures
The remedies to wire breakage are: reduction of prestress, usage of a different wire material (e.g.carbon fiber will withstand the beam intensity and the prestress), and the scan speed increase.
The solution currently applied is the installation of a thinner wire, which leads to lower temperatures.A wire with a diameter of 13 µm was successfully used to scan the beam.However, the calculations show that it will suffer from the same breakage but after a higher number of scans.

Other damage mechanisms
Material melting was observed, for example, in the case of LEP beryllium wires [11], where the wires were heated due to coupling to the beam RF field.Electrical discharges between the tungsten wires and a support stud were found responsible for the damage observed on the SLAC scanners [12].
In vacuum, the vapor pressure of the materials is very low, leading to high sublimation rates.The case of carbon fiber was studied in a series of measurements at CERN [13].Due to the stabilizing effect of the thermionic emission on temperature, it was possible to gradually sublimate the wire material.Extreme sublimation, down to 4 µm (more than 90% of wire material), has been reported [3].The decrease in diameter leads to smaller heating and higher cooling mechanism performance, which makes carbon fiber a particularly good target.The sublimation process is relatively well understood and a good agreement between predictions and measurements has been reported [14].A new damage mechanism that leads to "blowing" of carbon nanotube wires was recently observed [2].The reason was tracked to the presence of iron impurities in the wire structure.

Conclusions
The mechanism of wire breakage used in the instrumentation of high-power hadron accelerators is presented.Analysis of the ductile breakage of the metallic wire shows how too high prestress affects its lifetime.Cracking in the wire surface due to plastic deformation is documented.An attempt to explain the sudden increase in thermionic emission by a decrease of the work function due to the plastic strain of the wire is plausible, but additional measurements are needed especially to assess the emissivity deterioration.

Figure 1 .
Figure 1.Electron microscope image of molybdenum wire broken in proton beam at PSI transfer line.

Figure 2 .Figure 3 .
Figure 2. Observation of beam profile during a scan number 45, with the thermionic emission bump.

Figure 4 .
Figure 4. Thermionic current excess during series of scans performed on Aug 2, 2022 at constant beam current of 1.8 mA and other beam parameters.

Figure 5 .
Figure 5. Electron microscope images of pristine molybdenum wire (left) and a section close to the breakage location (right).

Table 1 .
Thin target material properties.For carbon fibre (CF) melting temperature is replaced by sublimation temperature and for SiC by chemical decomposition temperature.