## 1 Introduction  
In 1992, [PERSON] et al. theoretically predicted that apart from spin angular momentum, photons can also carry another form of angular momentum: orbital angular momentum [1]. It comes from the helical phase of light waves, i.e., a light beam with a phase term \(\exp(-il\varphi)\) (\(l\) is an orbital angular quantum number, which is also called topological charge (TC) and \(\varphi\) is the azimuth angle), and each photon carries an orbital angular momentum (OAM) of \(l\). Theoretically, \(l\) can be any integer or a fraction [2; 3; 4]. Laguerre-Gaussian (LG) and Bessel-Gaussian (BG) beams are two typical kinds of vortex beams. Another obvious feature of the vortex beam is that the spatial distribution of its intensity presents a 'donut' structure, i.e., its intensity at the center is zero, and the radius of the hollow center increases gradually with the increase of \(l\). The OAM carried by the vortex beams can be transferred to matters during the interaction of vortex beams and matters [5; 6]. These special properties make vortex beams widely applied in optical tweezers [7; 8; 9; 10; 11; 12; 13], optical imaging [14; 15; 16], information transmission and cryptography [17; 18; 19; 20; 21; 22] and micro-processing [23; 24; 25; 26] and other fields. For example, Bessel beams have propagation invariance compared with Gaussian ones; that is, they have the ability to maintain their shape and peak power at the extended focal region (Bessel region), which makes them have promising application prospects in many fields, especially for micro-processing. Using the Bessel beams, the length, plasma density and laser intensity of the femtosecond filament can be well controlled [27; 28; 29; 30], see Table 1. For example, [PERSON] et al. tailored the profile of the annular Bessel beams by placing an amplitude mask and iris diaphragm, respectively, before the axicon, and thus the onset and terminal positions of femtosecond laser filament in the fused silica can be arbitrarily controlled [28]. Once the parameters of femtosecond filament are controlled, they are accompanied by several nonlinear phenomena such as photoionization and supercontinuum (SC) generation; fluorescence emission is also affected [30; 31; 32]. For example, [PERSON] et al. studied the filamentation of Bessel beams in BaF\({}_{2}\) by measuring the side emitted fluorescence and transmitted SC [32]. They observed the transition from a stable state to a nonlinear unstable state for Bessel beams by changing the incident laser pulse energy and found that SC generation depends on the size of the incident beam and the distance from the sample to the tip of the axicon. However, these studies are limited to 0-order vortex beams. For higher-order vortex beams, they carry OAM, which will increase the complexity of the filamentation process. As they propagate in a transparent medium, they have a great chance to split into multiple filaments [33; 34; 35; 36], thus affecting the filamentation dynamics. In addition, the filamentation threshold of the higher-order LG filament increases with TC, which can be roughly described by \(P(l)\approx 4\sqrt{3}lP_{cr}\), where \(P_{cr}=\frac{3.77/2}{8\pi m_{0}l_{2}}\) is the critical power of self-focusing for Gaussian beams [34; 35]. [PERSON] et al. found that by using coherent conjugate asymmetric higher-order BG beams to control the far-field intensity distribution, the filamentation process can be spatiotemporally controlled [37]. [PERSON] et al. experimentally and numerically studied the nonlinear propagation of higher-order BG light in transparent solids [38] and found that higher-order BG beams retain all the properties of 0-order BG beams, while the TC provides additional parameters which can control the filamentation of BG beams. They also found that the radius and plasma density increase with the increase of TC value and top angle [38]. [PERSON] et al.