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Subsequent phases of evolution could in principle regenerate a strong magnetic field in the core if an efficient dynamo is at work. The turnover timescale in the convective He-burning core is about 10-20d, while the asteroseismic inferred rotation rates are in the range 30...250 d. This means that Rossby numbers ($Ro$) are in general larger than 1; however for some He-burning cores $Ro$ could be close to 1, potentially allowing for an efficient $\alpha\omega-$dynamo. The core magnetic field in that case could reach an equipartition value on the order $10^6-10^7$ G. Note that this field would be probably confined to the convective core and do not affect the g-mode cavity, so it would not be probed by the dipole modes.   At the end of the core He-burning phase, when convection disappears the generated magnetic flux could end up in a stable configuration. Since the Ohmic timescale is way longer than the remaining lifetime of the star (this is actually true during any evolutionary phase for stars of mass above $1\mso$) this dynamo-generated magnetic field could survive till the white dwarf (WD) stage. Assuming conservation of magnetic flux, the change in radius of a factor of 10 implies a factor of 100 in B, resulting in a maximum magnetic field of B=$10^8-10^9$ G for the WD. Fields higher than $10^6$ G are indeed observed in 8-16\% of WD \citep{Liebert_2003,Kawka_2007}; the most magnetic WDs have B$\approx10^9$ G.   Since the number of Ap stars during the main sequence is about 10\%, it is tempting to imagine that this broadly represents the chance of a convectively generated magnetic flux to land a stable magnetic configuration when convection disappears. Since a stable configuration requires a certain degree of interlocking between the toroidal and poloidal components of the magnetic field \cite{Braithwaite_2006}, magnetic helicity is probably the important quantity determining if an initial configuration of the field can evolve into a stable equilibrium. However, since being  convection is an  inherentlya  stochastic process (and helicityis  conserved only in ideal MHD) it is not obvious how to build a predictive theory given the stellar observables. In absence of such theory, it is probably fair to just assume that $\sim10\%$ is the probability of getting a stable field after some dynamo action in a convective core (or in the whole star, as during the convective pre main sequence).