As an emerging and extraordinary plasma source, the bipolar-pulse high power impulse magnetron sputtering (BP-HiPIMS) has promising prospects and wide industrial applications. In this paper, an effort to optimize the plasma flux and energy in BP-HiPIMS via auxiliary anode and solenoidal coil was made. This novel plasma source contains two types of auxiliary anode voltage (direct current and pulse) and one type of solenoidal coil current (direct current) to synergistically enhance the plasma generation and diffusion by electric field and magnetic field together. Systematic evaluations of discharge characteristics demonstrate that applying auxiliary anode voltage and coil magnetic field effectively contribute to a reduction in delay time of target current onset and increase in peak amplitude of target current, which are beneficial for improving plasma generation and target sputtering. The complex plasma dynamics are diagnosed by Langmuir probe and optical emission spectroscopy, and simulated by particle-in-cell/Monte Carlo collision approach. These comprehensive investigations on plasma parameters demonstrate that the plasma density, emission intensity of the metal ions, substrate current density, and ionization fraction of sputtered target particles have been improved with the increase of coil current. The observations of the increase in excitation temperature T exc of Ar atoms, and more extended high-energy tails in electron energy distribution function curves imply that the plasma can be significantly heated by the auxiliary anode. Combining the simulation results and theoretical model proposed in the last sub-content, the diffusion and transport mechanism of charged-particles in complex electric and magnetic fields are discussed. From the theoretical analysis, the qualitative relation between the plasma density and coil current is well consistent with the measurements of electron density obtained by Langmuir probe. These evidences all support the idea that the plasma flux and energy can be enhanced in BP-HiPIMS discharge via auxiliary anode and solenoidal coil together.