## 1 Introduction  
Proton acceleration by the interaction of an ultra high intensity laser beam with matter is very important for basic science and has several wide prospective applications, including cancer treatment,nuclear physics and astrophysics in lab, (see [1; 2; 3] for review). In recent years, several promising acceleration schemes were suggested and demonstrated, among them Target Normal Sheath Acceleration (TNSA) [4; 5], Radiation Pressure Acceleration (RPA) [6; 7] collisionless shock acceleration [8] and Break Out Afterburner (BOA) [9]. A variety of schemes aimed to increase the interaction efficiency were proposed such as mass-limited targets [10] and nano-structure targets [11; 12; 13]. The above accelerating schemes are optimized for interaction between the high intensity main laser pulse and a cold solid-density target, and are strongly degraded as the main laser pulse interacts with a pre-heated or ionized target caused by a prepulse. Therefore, a huge experimental effort is focused in reducing the energy in the prepulse, _i.e._, contrast ratio of the order of 10\({}^{-11}\) for 100 TW laser system and even higher for more energetic systems. Recently, we have demonstrated an alternative approach to laser-based proton acceleration by using a moderate power laser system and micro-structured snow targets [14; 15; 16]. These targets were engineered by depositing snow on sapphire substrates. It was shown that pre-formed plasma formed by a prepulse may be beneficial to the acceleration process [17; 18]. Our experimental results [16] show that the energy of the accelerated protons scales with the power of the laser according to \(E_{\mathbf{p}}\!\sim\!\!P_{L}^{1/2}\), like other schemes [19] (see Figure 1). Using structured snow targets and relatively low contrast ratio this scaling was demonstrated for significantly lower laser powers than the traditional schemes [14; 18]. Moreover, in experiments that were carried out at laser system with high contrast ratio (short pulse prepulse with energy below microjoule), where the main pulse interacted directly with solid snow surface, the protons were accelerated to much lower energy [14; 15; 16]. The high proton energy can be attributed to combination of several effects: The improved laser absorption [18] and the interaction of the laser with mass limited plasma with density gradient induced by the prepulse lead to significant enhancement of its effective electrical field [16]. In addition, field enhancement at the tip of snow micro-structures and their curved surface may enhance as well the interaction, leading to higher proton energies. Figure 1: Energy scaling of the accelerated protons as a function of the laser power on target. The various points describe data obtained by many contributors (reproduced from [19]), the experimental results obtained with snow targets are marked by black circles. Results of PIC simulations are marked by blue diamonds (Reproduced with permission from [16]; published by American Physical Society, 2013). Numerical 2D particle in cell (PIC) code simulations [16], with initial conditions given by the state of the plasma snow at the time of the interaction with the main pulse in the experiments, reproduced the obtained proton energy and explained the crucial role of the dynamic plasma produced by prepulse illumination of the snow target. For laser powers greater than 100 TW, the simulation predicts proton energy near 150 MeV. In this paper, we further explore the role of the dynamic plasma generated by the prepulse in our approach to laser-induced proton acceleration based on snow structured targets and moderate power (\(<\)10 TW) laser systems. These aspects of the work are published for the first time. Section 2 describes the morphology of the snow targets and presents measurements of their optimal damage threshold (ODT) aimed to understanding and controlling the prepulse produced plasma parameters.