Exploring the Role of Vector Potential and Plasma-$\beta$ in Jet Formation from Magnetized Accretion Flows

In this work, we investigate how the choice of initial vector potential and plasma parameters influences the development of accretion columns and jet formation in magnetized accretion flows. Using general relativistic magnetohydrodynamic simulations, we explore two different configurations of the vector potential $A_{\phi}$ and three plasma beta values $\beta$ = 50, 100, 500. We analyze how variations in the poloidal magnetic field strength and plasma magnetization affect magnetic flux accumulation near the black hole and the subsequent growth of the accretion column. Our results highlight the dependence of jet launching efficiency and accretion dynamics on the initial magnetic field topology and plasma beta, offering insight into the conditions that favor magnetically arrested disk or standard and normal evolution states.