= Solution
An <Asymptotic giant branch> star has an approximately degenerate carbon-oxygen core, a helium-burning shell, a hydrogen-burning shell farther out, and a deep convective envelope. During an interpulse interval, the <hydrogen-burning shell> supplies most of the luminosity and deposits helium ash beneath it. The helium layer gradually grows and its temperature rises until <Triple-alpha process> heating becomes large.
The helium layer is geometrically thin. A thermal perturbation greatly increases its nuclear rate, but at first expansion of the layer does not provide sufficient cooling to offset the heating. This <Härm–Schwarzschild instability> causes a <thermal pulse of an asymptotic-giant-branch star>: a helium-shell flash with an enormous but brief increase in internal helium luminosity. It is a shell instability, not repeated ignition of the entire stellar core.
The flash creates an intershell convection zone, expands the layers above it and cools or extinguishes hydrogen burning temporarily. Much of the flash energy goes into expansion and internal rearrangement, so the huge peak shell luminosity need not immediately appear as a comparable surface luminosity. After the layer expands and cools, the helium flash subsides; hydrogen burning later resumes and replenishes the helium layer, repeating the cycle.
After a pulse, the convective envelope may penetrate into the intershell: <third dredge-up> transports newly formed carbon and <slow neutron-capture process> products to the surface. This helps explain carbon stars and heavy-element enrichment. Strong winds remove the envelope over successive pulses. When the envelope is too small to sustain the giant configuration, the star leaves the AGB and exposes a hot core that becomes a <white dwarf>. Pulse behavior, dredge-up efficiency and the number of cycles depend on core/envelope mass, composition and mass loss.
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