## 4 Discussion  
A parabolic trough mirror is typically a continuous and complete parabolic trough mirror with significant manufacturing error, resulting in a large concentrated light spot, reduced optical efficiency and ultimately lower net efficiency [36]. Additionally, the tube receivers commonly used in these conventional trough solar collectors can reach higher temperatures due to higher concentration ratios, which leads to cracks in tube receivers in the long term, further diminishing the overall efficiency of solar collectors; in contrast, cavity receivers are developed to reduce thermal losses through convection and can achieve higher efficiency, thereby enabling operation at higher temperatures [18]. This work proposes a novel parabolic trough solar concentrator made with spliced cylindrical mirrors, in which the cavity receiver is applied. By limiting the width of the cylindrical mirror for a spliced parabolic solar collector, we significantly reduced the spherical and coma aberrations to minimal impact on the overall system performance, which can be ignored in most cases. Conventional parabolic solar collectors have significant challenges in manufacturing, and the resulting parabolic mirrors are known to have higher slope errors, which can reach up to 8 mrad [36]. In contrast, cylindrical mirrors, under similar manufacturing conditions, are easier to produce and can achieve lower slope errors, typically between 1 and 2 mrad [33]. Our results indicate that the annual average interceptor for optimized design achieved is 94.6%. Compared with data from conventional trough intercept experimental tests, it lies within the range achieved by practical parabolic solar collectors and experiment results described by other researchers. For example, for incidence angles between 10 and 40 using north-south tracking systems in California and Spain, the measured intercept factor was between 93% and 97.5% [37]. Although, the cylindrical mirror-spliced system may achieve an average annual interceptor of at most 2.9% lower than that of the best of the conventional trough system over a year, considering that the optimized system with cylindrical mirrors has a higher concentration ratio, which is about 50, leading to  
Figure 8: The annual average net efficiency of three types of trough solar concentrators under north–south axis tracking mode in the year 2020, with slope error \(\theta_{slope}=1\) mrad (cylindrical mirror)/3 mrad (trough mirror). nearly half the heat loss of the conventional trough system and higher net energy efficiency. Our results indicate that the new system can achieve 65% annual net energy efficiency, compared to 51% of a conventional parabolic system. When employing circular mirrors, such as spliced cylindrical mirrors as replacements for parabolic mirrors, the critical issue to address is the spherical aberration associated with circular mirrors because their constant curvature means light rays hitting different parts of the mirror do not focus at the same point, and rays converge on the focal plane instead of the focal line, resulting in aberration. Aberration theory points out that, in [PERSON]'s \"Research and Testing of Optical Systems\" [30], the relative aperture of a spherical reflector as the primary mirror should not exceed 1:10.8, which means that the ratio of the reflector aperture to the focal length is \(\leq\)1/10.8, which is then converted to the ratio of the reflector aperture to the spherical radius \(\leq\)1/21.6. Our research has shown that when using both a tube receiver and cavity in a cylindrical mirror-spliced parabolic solar collector, the condition for reducing spherical aberration is that the transverse spherical aberration should not exceed 5% of the trough radius. Therefore, the condition for reducing spherical aberration is w/r \(\leq\)1/5; since r = 2f, this can be converted to w/f \(\leq\) 1/2.5, which is much easier to achieve in practice than the typical requirement of 1/10.8 in the field of optical imaging.