Javascript Prototypes that represent HTML elements
As dystroy mentioned, the setters and getters are really not JavaScript style, neither are the many try/catch statements in your functions.

However, if you insist on having all these getters and setters, you should create a utility function that generates a getter/setter  for you. Since you have default values for most properties in your LightParticle I was thinking something along the lines of this : 

function addGetterSetter( o , property , defaultValue ){
  var postFix = property[0].toUpperCase() + property.slice(1),
      getter  = 'get' + postFix,
      setter  = 'set' + postFix;
  o[getter] = function(){
    return this[property] || defaultValue;
  }
  o[setter] = function( value ){
    this[property] = value;
    return this;
  }  
} 


And then you would

var LightParticle = function() {},
    prototype = LightParticle.prototype;

addGetterSetter( prototype , width   , 10 );
addGetterSetter( prototype , height  , 10 );
addGetterSetter( prototype , top     , 0 );
addGetterSetter( prototype , left    , 0 );
addGetterSetter( prototype , position, 'absolute' );
addGetterSetter( prototype , background, 'white' );
addGetterSetter( prototype , className , 'LightParticle' );