In present-day single-rod/single-beam solar laser systems, the thermal lens effect is a serious issue that limits its ability for a scale-up to higher powers and improved beam quality. Aiming at resolving this shortcoming, the concept of a seven-rod/seven-beam solar pumping scheme is proposed. This scheme was composed of a first-stage heliostat-parabolic mirror system and a single large laser head. The large laser head consisted of seven fused silica compound parabolic concentrators, which transmitted and focused the concentrated solar radiation to each single-laser rod of small diameter, within a conical cavity, which enabled multiple passages of the pump rays. Consequently, each laser rod was pumped by only one-seventh of the total concentrated solar power, ensuring a significant reduction of the thermal induced effects in the laser rods. 13.3  W/m² TEM₀₀-mode solar laser collection efficiency was numerically achieved, representing an enhancement of 1.68 times over the experimental record from a single-rod prototype. 1.80 times improvement in solar-to-TEM₀₀-mode laser power conversion efficiency was also registered in relation to the previous experimental record.