2.8 Acceleration in Plasma Wakefields
2.8.3 Plasma Torch Injection
In laser-driven plasma-wakefield acceleration schemes, density gradients are normally genera-ted hydrodynamically for example with razor blades or knife edges as gas-flow obstacles that are positioned on top of gas jets [83,84,85]. This hydrodynamic approach is required because of the specific electric-field and laser-intensity parameters in typical LWFA. Because the laser excites the plasma wake by its ponderomotive force, which scalesF ∝ I ∝ E2, it needs to be very intense to drive a plasma wake and the laser-electric fields are so high that they fully ionize the gas in most cases. An effective plasma density shape can therefore not straightfor-wardly be produced by generating a plasma density profile with a preionization laser and a gas density downramp is necessary.
In PWFA, the transverse force scales withF∝E, so that the electron beam needs much lower electric fields in order to drive a plasma wake. Ionization of a gas due to the driving electron beam can be avoided with negligible effect on the wake, which is why in PWFA, electron density gradients can be generated by locally controlling the ionization level of the plasma.
Our alternative approach is the optical generation of a plasma density spike, also called a Plasma Torch[8,9] as the means to inject an electron bunch. We make use of the ionization gap explained in the chapter2.3to use a HIT and LIT medium for distinct plasma shaping by applying two laser arms with different levels of intensity. There are a number of possible gas
Figure 2.10: Sketch of a Plasma Torch injection setup taken from reference [9]. A pre-ionization laser arm generates a plasma on the electron-beam axis, ionizing only the H2 of the H2/He gas. A second injection laser arm ionizes a small density spike on axis by ionizing He in a confined volume with sharp density edges.
mixtures that can be used to ensure a sufficiently large ionization gap. In this work, we will only focus on the combination of helium as HIT and hydrogen as LIT medium (see figure2.2).
The plasma electron density shape and profile is determined by the laser pulses that ionize gas prior to the arrival of the driving electron bunch. This shape is generated over timescales down to few femtoseconds – the duration of the laser pulses – but it then is present over timescales eventually determined by the plasma recombination time, which is typically on the order of a few ns. Therefore, picosecond control over the relative time of arrival between the electron beam and the laser pulses is already sufficient to ensure that the electron bunch propagates through the desired density profile.
Figure2.10 shows a sketch of the proposed setup [9]. A pre-ionization laser pulse ionizes a long plasma column and only ionizes the hydrogen gas to a homogeneous plasma along the electron-beam orbit. A second laser is focused down perpendicular to the beam propagation axis with higher intensity than the pre-ionization laser to ensure full He ionization in a confined volume. Both laser arms need to ionize the gas prior to the arrival of the electron bunch. Due to the exponential dependence between ionization rate and electric field, density downramps on the order of10µmlength can be formed and picosecond-timing control ensures these profiles persist until the electron beam arrives. The gradients can be tuned very easily by changing the relative density of hydrogen and helium.
20 40 60 80 100 120 140 160 180 0
0.5 1 1.5 2 2.5 3 3.5
20 40 60 80 100 120 140 160 180 0
0.2 0.4 0.6 0.8 1 1.2 1.4 1.6
ne / 1017 cm-3
20 40 60 80 100 120 140 160 180 0
0.5 1 1.5 2 2.5 3
3.5 nHe= nH2, ntot,0= nHe+ nH2
nHe= 4 nH2 nHe= 4 nH2, ntot = 2.5 ntot,0
Plasma density profile w/o pre-ionization
5 mJ Gaussian Laser intensity Plasma density profile with pre-ionization
I / 1015 W cm-2 ne / 1017 cm-3
z / µm z / µm z / µm
a) b) c)
Figure 2.11:Part a) shows the calculated focal intensity distribution of a Gaussian laser pulse with 5 mJ energy, a pulse length of 20 fs FWHM and at 800 nm wavelength. The corresponding plasma density profile, calculated with ADK rates in a 1:1 H2:He gas mixture, without ionization is shown in part b). Image c) shows the plasma-density profile in the case of pre-ionized hydrogen at different gas properties. A plasma density profile for a H2to He gas mixture ratio of 1:1 (blue), 1:3 (red) and 1:4 at a total gas density increased by a factor of 2.5 (yellow) is plotted. The blue graph in part c) shows the same density and ratio as part b).
Figure2.11shows an example of possible plasma density spikes and control by relative and ab-solute HIT and LIT densities. The focal intensity distribution of a 5 mJ, 20 fs, 800 nm laser pulse and the corresponding density profiles are shown. Figure2.11 b) shows the laser transverse density distribution calculated from tunnel ionization (eq.2.52) in the case that there is no pre-ionization laser and assuming that the injection laser ionizes hydrogen as well as helium.
The outer wings in the distribution are caused by the lower ionization threshold for hydrogen.
In this example, both gases have the same molecular gas density and the total molecular gas density isntot= nH2+nHe=1× 1017cm−3.
Figure2.11 c) shows how the density profile can be controlled in the case of two lasers, by changing the total gas density and the ratio between the molecular density of the gas com-ponents. The pre-ionization laser is assumed to fully ionize hydrogen and not to ionize the helium gas. If one starts with the density profile shown by the blue plot and wants to increase the density of the upper plateau while leaving the rest of the plasma density constant, chan-ging the gas mixture only is insufficient. Chanchan-ging from the 1:1 gas mixture (blue) to a 1:4 ratio between molecular hydrogen and helium at the same total gas density (red) leads to a decreased plasma density of the lower plateau before and after the plasma density spike. The total gas density needs to be increased by a factor of 2.5 to bring the lower-plateau plasma density back to1×1017cm−3. With these two parameters, the gas density and mixture ratio, the plateau plasma densities can be arbitrarily adjusted without changing the laser, which lea-ves the possibility to change the form of the downramp independently by modifying the laser properties.
In order to use the gas densities to control the ramp gradients, it is a necessity that the HIT and LIT media are not the same gas or that the HIT medium does not have a lower ionization energy
that is smaller than or equal to the ionization energy of the LIT medium. For example, Li and H2are two distinct gases, and the transitionLi+ → Li2+has a large ionization gap, but the ionization energy for the transitionLi→Li+is even lower than for hydrogen. Therefore, the pre-ionization laser, if at the right energy to ionize hydrogen, will always additionally ionize the first level of Li and an independent density gradient regulation as previously described is no longer possible. In [8] and [9], the option of a Plasma Torch Injection for an electron bunch for the experiments described in chapter5was explored. Assuming a driver bunch with an energy ofW = 23 GeV, an rms bunch length of σz = 27µm and a radial rms size of σr =8.5µm, the charge was varied betweenQ=1 nCandQ=3 nC. The emittance was set toen =2.25×10−6mrad. Three cases were studied:
1. Gaseous H2only, no preionization laser.
2. Gaseous H2/He mixture, no preionization laser.
3. Fully ionized H2, He ionized locally by the injection laser.
Cases 1 and 2 rely on ionization by the drive bunch. In these cases, injection occurs due to a sudden shift in wake phase velocity, which is caused by two effects. The first is from the plasma density transition because the drive bunch is not capable of fully ionizing a large column of gas to a plasma in case 1 and does not ionize He at all for case 2 so that the effective electron-beam-ionized plasma density is smaller than the density in the plasma torch volume. The second effect that causes a wake phase-velocity shift is the fact that in the plasma spike, the wake forms in plasma that does not need to be generated by the electron bunch. The bunch ionization in the gaseous environment shifts the ξ onset position of the wake upstream; this sudden shift also acts as a transitory phase-velocity decrease which allows for the injection of sheath electrons9. With a3 nCdrive bunch for case 1 and 2, injection of up to530 pCwas observed with an approximately linear relationship between torch plateau plasma density and injected charge. Simulations of case 3 generated the witness bunches with lowest emittance (2.6× 10−6mrad) and even forQ=1 nCdrive-bunch charge, a total charge ofQW=260 pCcould be accelerated.