# Quick Response Circulating Water Cooling of \(\pm\)3 mK Using Dynamic Thermal Filtering
## 1 Introduction  
Thermal management using circulating cooling water (CCW) is essential for precision manufacturing [1]. With precision manufacturing stepping into a nano-era, the challenging demand for CCW with mK level stability and a quick response is put forward by a variety of ultraprecision applications, such as ultraprecision optical machining with nanometer accuracy, and lithography which is stepping to a 7 nm technical node [2, 3]. In an advanced lithography machine, CCW with a temperature stability of \(\pm\) 0.01 K is required to cool down power devices like motors, power drivers, laser sources, and so on [4, 5], especially to maintain a \(\pm\)0.01 K temperature stability of objective lenses. Moreover, CCW is also used as a temperature reference medium to produce an 'air shower' of temperature stability, up to 2.3 mK/5 min, for air refractive index stabilization of laser interferometry. Meanwhile, a response time of CCW temperature control as short as dozens of seconds is demanded to suppress the cyclic thermal pollution of power devices in lithography. Similar requirements are also presented in ultraprecision optical machining. CCW with a temperature stability of \(\pm\)0.1 K is needed to cool down electrical spindles [6, 7], and the temperature of CCW needs to dynamically respond to the variation in rotation speed of spindles, and thus to realize'servo' thermal pollution management of the spindles.  
One effective technical route to achieve high temperature stability of CCW is to reduce the temperature fluctuation by increasing thermal inertia. [PERSON] et al., proposed a method to reach this goal through heat exchanging with an additionally introduced thermal capacity medium, such aswater, and stainless steel balls [8; 9]. Phase change material (PCM) has also been utilized, because of its large latent thermal capacity at the phase change temperature point [10; 11; 12]. However, the proposed methods only function in the very narrow range of the preset temperature point of the introduced thermal capacity medium, or the phase change temperature point of PCM. Therefore, they can only reduce the CCW temperature fluctuation in static water-cooling applications in which the output temperature of CCW is required to be constant.  
New control schemes and algorithms have also been presented to improve the temperature stability and dynamic performance of CCW. For example, [PERSON] et al., and [PERSON] et al., proposed temperature controllers achieving temperature stability at sub-millikelvin level [13; 14; 15]. However, the response time of CCW temperature control in these studies ranged from tens of minutes to hours, because the dynamic performance was not taken into consideration. [PERSON] et al., proposed a'servo' temperature control method for the cooling of spindles of precision machining tools [16]. Two CCW streams from two CCW machines with different temperature set values were used, then temperature of the mixed CCW was proportional to the mixing proportion of the two streams. Temperature stability at sub-kelvin level and a quick response of CCW temperature control were realized, at the cost of using two CCW machines and a complex flow rate control.  
Therefore, it is difficult to simultaneously achieve high temperature stability and quick response of CCW temperature control. CCW with temperature stability at mK level and a response time at \(\sim\)100 s level is still a challenging demand for precision manufacturing. Thus, this paper proposes an enhanced CCW machine using a dynamic thermal filtering method (DTFM) and bidirectional agile thermal control to solve this problem.