The concept of a "quantum vacuum inside a quark" is not well-defined in the context of our current understanding of particle physics. Quarks are elementary particles that are considered to be fundamental constituents of matter, and they are not believed to possess any internal structure or contain smaller particles within them.
In quantum field theory, which is the framework used to describe the behavior of elementary particles, the vacuum is defined as the lowest energy state of the quantum fields that permeate all of space. These quantum fields, such as the electromagnetic field or the Higgs field, are associated with their respective particles. However, it's important to note that the vacuum is not a "void" or an empty space but rather a state with fluctuations and virtual particle-antiparticle pairs constantly appearing and disappearing.
Quarks are subject to the strong nuclear force, which is described by the theory of quantum chromodynamics (QCD). In QCD, quarks are bound together in composite particles called hadrons (such as protons and neutrons) by the exchange of gluons. The interactions between quarks and gluons are described by a complex mathematical framework that involves the quantum field theory of QCD. However, the notion of a vacuum inside a quark is not part of this description.
Therefore, within the current understanding of particle physics, it is not meaningful to speak of a specific type of quantum vacuum inside a quark.