You know that stars are much, MUCH bigger than planets and therefore destroying a planet should be 'piece of cake' when you can destroy a star!?
Explanation 1: The Terror Star is a directed Artificial Gravity weapon. The primary weapon must be able to penetrate to the core of a star for maximum effect, and therefore due to the extremely low mass of planets, such directed energy simply passes right through them. The weapon's purpose is to simply artificially increase the mass of the stellar core until it passes the Chandrasekhar limit. Then - Kerplooie!
Explanation 2 (My personal choice): Most all planetary cores are made of elements of iron or heavier. Nearly all these mundane elements have high binding energy and therefore CONSUME energy when fusion or even fission takes place.
Nearly all stars are composed of elements lighter than these elements, including helium, oxygen, and carbon.
Imagine the Terror Star's weapon works by breaking the nucleon binding forces in lightweight atoms, therefore, those found in great numbers and density, like in a star. Breaking these bonds and allowing them to instantly refuse, and repeating this action will release a tremendous amount of energy, causing the core of the star to swell dramatically. When the beam is no longer applied, the core contracts dramatically, causing an exponential increase in temperatures and pressure, which in turn causes a chain-reaction. The core of the star begins to nova as massive pockets begin advanced fusion. Such massive releases of energy cause rapid expansion and collapse all over, and the core literally begins bouncing off itself.
This runaway process simply causes the star to tear itself apart.
Such a weapon, if used on a planet, would have minimal effect on the core, and only lightly interact with the atmosphere. Due to the extremely low density of these lighter elements in the upper atmosphere, it would likely have zero noticable effect.
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