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The Main Sequence is, by definition, where stars convert hydrogen ---> helium in their cores. On the Main Sequence, massive stars generate energy through hydrogen burning using the CNO cycle. On the Main Sequence, the L of a massive star slowly increases while its surface T decreases (the star moves to the right and up in the HR diagram). After the core is cleaned out of hydrogen, the core starts to cool and contract slowly. As the core contracts, it heats up and increases in density. This slow contraction causes the surface of the star to become hotter and slightly more luminous (the star moves to the left and up in the HR diagram). As the core contracts and heats, the region just outside the core gets heated by the shrinking core. Since the region just outside of the core has abundant hydrogen, when its temperature reaches several million K, hydrogen burning is ignited in a shell outside the core. The formation of this shell source causes the overall star to expand and cool (the star moves to the right in the HR diagram).
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At this time the core is still inert (a slowly contracting ball of helium). When the core finally reaches a temperature of ~ 200,000,000 K or so, helium burning is ignited. This occurs at the tip of the Red Giant branch. The helium burns through what is called the Triple Alpha Process.
The ignition of helium causes a decrease in L and an increase in T (causing the star to move down and to the left in the HR diagram). The star settles in this burning stage for a time roughly 10 - 20 % as long as its Main Sequence lifetime.
The star then merrily cruises along in this state (helium burning in its core, surrounded by a hydrogen burning shell) until it scours the helium out of its core. The core of the star then cools, and starts to contract in an attempt to replace the heat lost by radiation from its surface. (This causes the star to start moving to the right in the HR diagram again).
Now, just as before when the contracting core heated the surrounding region and caused the ignition of hydrogen in a shell, the contracting core heats the surrounding helium and ignites helium burning in a shell. The star moves again rapidly to the right in the HR diagram.
When the conditions become right for convection to set in, the star rapidly increases in L (and moves almost vertically in the HR diagram). It ascends what is referred to as the Asymptotic Giant Branch (AGB).
It moves up the AGB until the core contracts enough to raise its temperature to the carbon ignition point at the tip of the AGB. When it ignites carbon, the star stops moving upward. Note--the lifetime of the carbon burning state is hundreds of years. This is too fast for the star to make any appreciable changes in its overall structure and so the outward appearance of the star does not change during carbon burning.
When the carbon is scoured out of the core, the core contracts until it can start carbon burning in a shell around the core and neon burning in the core. The neon burning lasts ~ 1 year and so the outward appearance of the star does not change during this phase of evolution.
For stars around 10 MSun, the process stops here. For more massive stars, the nuclear game continues to oxygen burning to silicon burning with the total time required for these phases being less than 1 year and so outward evolution of the star does not occur for these stages.
After silicon burning, the star has an iron (Fe) core surrounded by many active shell sources. The nuclear game stops at this point for stars of any mass. The star runs out of nuclear energy sources and is poised for a catastrophic event, the Type II Supernova event.
Illustrative numbers for the evolution of a 25 MSun star.