10K Pulse Tube Cooler
A 3-stage pulse tube cooler has been designed to operate at 10¶K. The staged cooler uses the same compressor and parallel staging configuration for the 1 st and 2 nd stages as previously employed for our delivered High Capacity Cryocooler (HCC). The 2 nd and 3 rd stages are in a serial configuration. The addition of the third stage extends the performance of this cooler to lower operating temperatures below 10¶K.
10 K high frequency pulse tube cryocooler with precooling
Abstract A high frequency pulse tube cryocooler with precooling (HPTCP) has been developed and tested to meet the requirement of weak magnetic signals measurement, and the performance characteristics are presented in this article. The HPTCP is a two-stage pulse tube cryocooler with the precooling-stage replaced by liquid nitrogen. Two regenerators completely filled with stainless steel (SS) meshes are used in the cooler. Together with cold inertance tubes and cold gas reservoir, a cold double-inlet configuration is used to control the phase relationship of the HPTCP. The experimental result shows that the cold double-inlet configuration has improved the performance of the cooler obviously. The effects of operation parameters on the performance of the cooler are also studied. With a precooling temperature of 78.5 K, the maximum refrigeration capacity is 0.26 W at 15 K and 0.92 W at 20 K when the input electric power are 174 W and 248 W respectively, and the minimum no-load temperature obtained is 10.3 K, which is a new record on refrigeration temperature for high frequency pulse tube cryocooler reported with SS completely used as regenerative matrix.
Asymptotic Properties of Solutions to Second-Order Difference Equations of Volterra Type
<jats:p>We consider the discrete Volterra type equation of the form <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" id="M1"><mml:mi mathvariant="normal">Δ</mml:mi><mml:mo stretchy="false">(</mml:mo><mml:msub><mml:mrow><mml:mi>r</mml:mi></mml:mrow><mml:mrow><mml:mi>n</mml:mi></mml:mrow></mml:msub><mml:mi mathvariant="normal">Δ</mml:mi><mml:msub><mml:mrow><mml:mi>x</mml:mi></mml:mrow><mml:mrow><mml:mi>n</mml:mi></mml:mrow></mml:msub><mml:mo stretchy="false">)</mml:mo><mml:mo>=</mml:mo><mml:msub><mml:mrow><mml:mi>b</mml:mi></mml:mrow><mml:mrow><mml:mi>n</mml:mi></mml:mrow></mml:msub><mml:mo>+</mml:mo><mml:mrow><mml:msubsup><mml:mo stretchy="false">∑</mml:mo><mml:mrow><mml:mi>k</mml:mi><mml:mo>=</mml:mo><mml:mn mathvariant="normal">1</mml:mn></mml:mrow><mml:mrow><mml:mi>n</mml:mi></mml:mrow></mml:msubsup><mml:mrow><mml:mi>K</mml:mi><mml:mo stretchy="false">(</mml:mo><mml:mi>n</mml:mi><mml:mo>,</mml:mo><mml:mi>k</mml:mi><mml:mo stretchy="false">)</mml:mo><mml:mi>f</mml:mi><mml:mo stretchy="false">(</mml:mo><mml:msub><mml:mrow><mml:mi>x</mml:mi></mml:mrow><mml:mrow><mml:mi>k</mml:mi></mml:mrow></mml:msub><mml:mo stretchy="false">)</mml:mo></mml:mrow></mml:mrow></mml:math>. We present sufficient conditions for the existence of solutions with prescribed asymptotic behavior. Moreover, we study the asymptotic behavior of solutions. We use <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" id="M2"><mml:mi mathvariant="normal">o</mml:mi><mml:mo stretchy="false">(</mml:mo><mml:msup><mml:mrow><mml:mi>n</mml:mi></mml:mrow><mml:mrow><mml:mi>s</mml:mi></mml:mrow></mml:msup><mml:mo stretchy="false">)</mml:mo></mml:math>, for given nonpositive real <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" id="M3"><mml:mrow><mml:mi>s</mml:mi></mml:mrow></mml:math>, as a measure of approximation.</jats:p>