Optical scheme for the CLON is depicted on Fig. 2 and 3. Requirements for optical scheme are:

1. rays incoming at angle ©A shall be reflected from end point of each zone to the opposite focus F2.

2. rays incoming at 0° shall be reflected by beginning point of each zone always to adjacent focus F1.

It can be shown that at suitable shape of the concentrator according to the criteria above, also other rays in the angular range defined and reflected by inner points of mirrors will always hit the receiver. Rays bounding the zone are in addition to those specified above these:

1. incomming at ©A and reflected by beginning point of zones

2. incomming at 0° and reflected by ending points of zones.

It is clear that if the receiver will be hit by rays reflected from beginning and ending points of a zone, all the rays between them will also meet surface of receiver. The same time, boundary point between two zones is always a beginning point of one of them and ending point of another. Details can be seen on fig. 3. Single reflection of this type of concentrator is satisfied by situation at © = 0° and reflection by beginning of a zone. If a ray is to be directed to the opposite corner (focus) F1 and all other rays within that zone must be with this rim ray parallel, not a single ray can be reflected before the focus F1 (on axis x), i. e. will never hit a lower placed zone (mirror).

Optical scheme shown on figures had undergo a transformation to geometry, by means of which final recursion formulas for calculation of the shape of mirrors has been derived. Number of mirrors is on selection of designer, as well as required acceptance angle (in accordance with required concentration level and tracking). Output area d defines the overall size of concentrator and do not affect to its shape. So each mirror can be then described by a pair of parameters — inclination ©i and length li, where i stands for index of current mirror. Recursion formulas for calculation of current mirror requires to know the parameters of all the lower (i. e. previous) mirrors:

Z l; COS © ;

©n = 90o — jarCtg^

Z i;s;n ©;

i=i

l = C°s(2Qn — QA — Qi) _dCOS(2Qn — Qa)

n “1 ; COs(©n -©A) COs(©n -©A)

Ending points of current mirror n can be calculated as

n

xn = Z l; cos ©

i=1

n

Уп = Zli sin0i

i=1

From equations above can be seen that it is not trivial to calculate the first zone at is has no predecessors. Length of first mirror can be obviously calculated by knowing the current (this time the first) inclination angle, but there is no prescription to calculate just the first inclination angle. It can be chosen, though it has been shown that there exist a range for selection, but concentrators with different angle ©1 and equal in all other parameters will differ in concentration factor C. Thus, in the set of solution there exist one which is supposed to be optimal. We need to find it in an optimisation process.

To optimize the concentrator according to C (also alternative for optimisation according to utilisation factor M has been laid under analysis) failed by analytic manner, thus it has been performed using numerical methods. It has been proved that such optimal solution exist and is unique. Aim of optimisation lies in maximisation of the function C = f (©1), i. e. it is necessary to find

sup {C (©1; ©a, n): ©1 є (0; 90°); ©A, n = const}

We assume that optimal inclination of the first zone will depend not only on acceptance angle ©A, but also on number of mirrors n. This means that number of mirrors must be known right before the optimisation run. From the said follows that it is not possible to add further zones later. Solution of optimisation will be searched in the form

©1 = f (©A; n), where n is taken as a parameter