| Abstract
| - Aims. We investigate the free magnetic energy and relative magnetic helicity injection in solar quiet regions. Methods. We use the DAVE4VM method to infer the photospheric velocity field and calculate the free magnetic energy and relative magnetic helicity injection rates in 16 quiet-Sun vector magnetograms sequences. Results. We find that there is no dominant sense of helicity injection in quiet-Sun regions, and that both helicity and energy injections are mostly due to surface shuffling motions that dominate the respective emergence by factors slightly larger than two. We, furthermore, estimate the helicity and energy rates per network unit area as well as the respective budgets over a complete solar cycle. Conclusions. Derived helicity and energy budgets over the entire solar cycle are similar to respective budgets derived in a recent work from the instantaneous helicity and free magnetic energy budgets and higher than previously reported values that relied on similar approaches to this analysis. Free-energy budgets, mostly generated like helicity at the network, are high enough to power the dynamics of fine-scale structures residing at the network, such as mottles and spicules, while corresponding estimates of helicity budgets are provided, pending future verification from high-resolution magneto-hydrodynamic simulations and/or observations.
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